G. Ausiello, G.F. Italiano, A. Marchetti-Spaccamela, and U. Nanni, "Incremental Algorithms for Minimal Length Paths," Proc. ACM-SIAM Symp. on Discrete Algorithms (1990), 12--21.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... algorithms and implemenatations have been tested on real world data instances (see e.g. 12] On top of that, incremental and dynamic methods have been developed to speed up the repeated solution of the SSSP on networks that are subject to minor changes from one iteration to the other (see [3, 10, 11]) Although weighted co interval graphs play an important role when solving scheduling problems (see [4, 7] for an introduction to interval and co interval graphs and applications) to our knowledge no specialized shortest path algorithm exists to solve this problem faster than in time (n 2 ) ....

G. Ausiello, G.F. Italiano, A.M. Spaccamela, U. Nanni. Incremental Algorithms for Minimal Length Paths. Journal of Algorithms, 12(4): 615-638, 1990.

.... p 1 INTRODUCTION HE capability of computing path queries is an essential feature in new database systems for many advanced applications such as navigation systems Geographical Information Systems (GIS) and computer networks [1] 2] 4] 5] [6], 11] 12] 14] 21] 22] 23] 24] 31] For example, one of the primary functionalities of Intelligent Transportation Systems (ITS) 10] 27] 28] 32] 33] is to find routes from the current location of a vehicle to a desired destination with a minimum cost (where cost could ....

....Agrawal and Jagadish [4] presented the disk based hybrid algorithms which combine the features of both matrixbased and graph based algorithms. A special access structure for transitive closure queries was proposed by [5] to improve the disk I O. Agrawal and Jagadish [3] Ausiello and Italiano [6], and Huang et al. 15] studied incremental algorithms for path computation. With the new computer architecture and computer network, the traditional algorithms were adapted to parallel and distributed transitive closure algorithms [11] 12] 14] 22] The capability of efficiently calculating ....

 G. Ausiello and G.F. Italiano, "Incremental Algorithms for Minimal Length Paths," J. Algorithms, vol. 12, pp. 615--638, 1991.

....proofs of correctness for these algorithms. In particular, within our framework, we propose two di erent incremental methods to transform static algorithms into new dynamic algorithms. The rst method when applied to the Dijkstra algorithm yields a dynamic algorithm similar to existing ones [10, 9, 15]. The rst method can also be used to transform other static algorithms (i.e. Bellman Ford) into their dynamic versions. The second incremental method yields new dynamic algorithms that are faster on average. Furthermore, with the second incremental method, the resulting dynamic algorithm will ....

....proofs of correctness for these algorithms. In particular, within our framework, we propose two di erent incremental methods to transform static algorithms into new dynamic algorithms. The rst method when applied to the Dijkstra algorithm yields a dynamic algorithm similar to existing ones [10, 9, 15]. The rst method can also be used to transform other static algorithms (i.e. Bellman Ford) into their dynamic versions. The second incremental method yields new dynamic algorithms that are faster on average. Furthermore, with the second incremental method, the resulting dynamic algorithm will ....

G. Italiano, A. Marchetti-Spaccamela, and U. Nanni. Incremental algorithms for minimal length paths. Journal of Algorithms, 12:615-638, 1991.

....proofs of correctness for these algorithms. In particular, within our framework, we propose two di erent incremental methods to transform static algorithms into new dynamic algorithms. The rst method when applied to the Dijkstra algorithm yields a dynamic algorithm similar to existing ones [11, 10, 14]. The rst method can also be used to transform other static algorithms (i.e. Bellman Ford) into their dynamic versions. The second incremental method yields new dynamic algorithms that are faster on average. Furthermore, with the second incremental method, the resulting dynamic algorithm will ....

G. Italiano, A. Marchetti-Spaccamela, U. Nanni, \Incremental Algorithms for Minimal Length Paths," Journal of Algorithms, vol. 12, 1991, p. 615-638.

....in O(n p log n) time. Recently in joint work with Rao and Rauch [4] we have given an O(n) time algorithm for computing single source shortest paths. However, in the dynamic realm this problem is much less well understood. Though there are many algorithms for the dynamic problem (see for example [5, 6, 7], see also [8] none of them can simultaneously handle both updates and queries in time that is sublinear in the input size. Definition 1 Let G be an n node planar undirected graph with nonnegative integral edge lengths. Let D be the sum of lengths. The length of a path from u to v (denoted as ....

G. Ausiello, G. F. Italiano, A. Marchetti-Spaccamela, and U. Nanni, "Incremental Algorithms for Minimal Length Paths," Proceedings of annual ACM SIAM Symposium on Discrete Algorithms (1990), 12-21.

.... procedure DynamicSWSF FP (G, U) declare G : a dependence graph of a set of SWSF equations U : the set of modified vertices in G u, v, w: vertices Heap: a heap of vertices preconditions Every vertex in V (G) U is consistent begin [1] Heap : [2] for u U do [3] rhs (u) g u (d (x 1 ) d (x k ) 4] if rhs (u) d (u) then [5] InsertIntoHeap( Heap, u, min(rhs (u) d (u) 6] fi [7] od [8] while Heap do [9] u : ExtractAndDeleteMin( Heap ) 10] if rhs (u) d (u) then u is overconsistent [11] d (u) rhs (u) 12] ....

....: a SSF grammar P : the set of modified productions in G GlobalHeap: a heap of non terminals preconditions Every production in G P is consistent. See Definition 5. 1) procedure recomputeProductionValue(p) declare p : a production begin [1] let p be the production Y g(X 1 , X k ) [2] value = g(d (X 1 ) d(X k ) 3] if (value d (Y) then [4] AdjustHeap( Heap (Y) p, value) 5] else [6] if p Heap (Y) then Remove p from Heap (Y) fi [7] fi [8] if (value d (Y) then SP (Y) SP (Y) p else SP (Y) SP (Y) p fi [9] if (SP (Y) then Y is ....

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Ausiello, G., Italiano, G.F., Spaccamela, A.M., and Nanni, U., "Incremental algorithms for minimal length paths," Journal of Algorithms, (12) pp. 615-638 (1991).

.... bad worst case complexity will have good amortized complexity only if there is something about the problem being updated, or about the way in which we update it, or about the kinds of updates which we allow, that precludes pathological updates from happening frequently [3] Thus, Ausiello et al. [1], for instance, use amortized cost analysis to obtain a better bound on the time complexity of an algorithm they present for maintaining shortest paths in a graph as the graph undergoes a sequence of edge insertions. However, in the fully dynamic version of the shortest path problem, where both ....

....already. We now verify that the algorithm does indeed maintain the invariants described above. Thus, we first need to show that all vertices satisfy the invariant whenever execution reaches line [8] The precondition guarantees that all the initially inconsistent vertices must be in U. In lines [1] [7] the algorithm creates a heap out of all the initially inconsistent vertices in the graph, and simultaneously the value rhs (u) is properly defined for every inconsistent vertex u. Hence the invariant holds when execution reaches line [8] for the first time. The loop in lines [8] 31] ....

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Ausiello, G., Italiano, G.F., Spaccamela, A.M., and Nanni, U., "Incremental algorithms for minimal length paths," pp. 12-21 in Proceedings of the First Annual ACM-SIAM Symposium on Discrete Algorithms, (San Francisco, CA, Jan. 22-24, 1990), Society for Industrial and Applied Mathematics, Philadelphia, PA (1990).

....smaller than L, for some given L. Then AGDP can be solved in space O(L 2 ) and time O(L 2 ) per edge insert operation. Proof: The space bound is immediate from the fact that the number of nodes in G and H is always O(L) The time bound follows from a simple observation due to Ausiello et al. [2]: Whenever an edge (p; q) is inserted, the distance function can be updated by comparing, for pair of nodes r; s, d(r; s) to d(r; p) w(p; q) d(q; s) where d denotes the old distance function. We conclude with the following theorem, which is the main result of this paper. Theorem 3.6 Suppose ....

G. Ausiello, G. F. Italiano, A. M. Spaccamela, and U. Nanni. Incremental algorithms for minimal length paths. J. of Algorithms, 12(4):615--638, Dec. 1991.

.... times for partially dynamic problems are as follows: for maintaining transitive closure with insertions, O(n) 8; 11] with deletions, O(m) 11] with deletions in acyclic graphs, O(n) 9] for maintaining shortest paths with insertions and positive integer weights no greater than b, O(nb log n) [1]. Klein et.al. give a fully dynamic algorithm for the allpairs shortest path problem on planar graphs. If the sum of the absolute values of the edge lengths is D then the time per operation is O(n 9=7 log nD) G. Ramalingham and T. Reps consider the problem of maintaining shortest paths in a ....

G. Ausiello, G. Italiano, A. Spaccamela, and U. Nanni. Incremental algorithm for minimal length paths. In Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 12--21, 1990.

....on centralized a route guidance system where TMCs can possess large main memory and high computation power, making the main memory path view approach feasible. Recently, there has been a body of literature on transitive closure computation and recursive query processing in the database community [1, 3, 4, 5, 6, 13, 14, 15]. While their works focus on secondary storage solutions, the benchmark studies in [3, 15] showed that the I O in computing all pair shortest paths becomes intolerable when the underlying graphs are cyclic with more than 300 nodes. If Shekar et al. s finding in [19] demonstrates that the current ....

Giorgio Ausiello, Giuseppe F. Italiano, "Incremental Algorithms for Minimal Length Paths," Journal of Algorithms, 12, 1991, pp. 615 -- 638.

....shortest paths in a graph. A one processor per node implementation of the heuristic updating phase of LCM could be viewed as an extension of their message passing algorithm where the single source is the dummy goal node of the augmented local graph. A similar algorithm is also presented in [1]. Deng and Papadimitriou [6] have considered the problem of exploring an unknown graph. Although their work is related, they only consider the task of exploring edges rather than nodes, and they concentrate on directed rather than undirected graphs. In addition, their work is only concerned with ....

Ausiello, G., Italiano, G. F., Spaccamela, A. M., and U. Nanni, Incremental Algorithms for Minimal Length Paths, in: Proceedings of the First ACM-SIAM Symposium on Discrete Algorithms, San Francisco, California (1990) 12-21.

....updates on the structure of the graph, while maintaining the possibility to answer queries on shortest paths without recomputing them from scratch. Various approaches have been considered in the literature to deal with dynamic shortest path problems both for single source and all pairs versions [2, 4, 6, 8, 9, 11, 12, 17], providing several non comparable solutions, each characterized by a given setting for (a) the kind of considered graph and edge weights, b) the set of allowed updates on the structure of the graph, and (c) the adopted measure of performances. The most general repertoire of update operations ....

....and far from being practical. In [3] the authors consider efficient dynamic solutions for bounded tree width graphs when the weight of edges might change, but without considering insertions and deletions of edges. An efficient solution for the all pairs incremental problem has been proposed in [2], assuming that edge weights are restricted in the range [1; C] One of the most important open problems in the field of dynamic graph algorithms is surely finding a fully dynamic solution for the single source shortest path problem for general directed graphs, with sublinear running time for ....

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G. Ausiello, G. F. Italiano, A. Marchetti-Spaccamela and U. Nanni, Incremental Algorithms for Minimal Length Paths, Journal of Algorithms, 12, 4 (1991), 615--638.

.... see [5,24] The best known semi dynamic data structure supporting insertions in digraphs with unit edge lengths uses O(n 2 ) space and has O(1) query time; the total time to process all edge insertions is O(n 3 log n) which amortizes to O(n log n) time per insertion for dense digraphs [3,20]. Regarding maximum flow, previous results are confined to the parametric maximum flow problem, where the capacities of the edges are functions of a parameter . In [13,16] it is shown that the value of a maximum flow for O(n) values of can be computed on line with the same time complexity as the ....

G. Ausiello, G.F. Italiano, A. Marchetti-Spaccamela, and U. Nanni, "Incremental Algorithms for Minimal Length Paths," Proc. ACM-SIAM Symp. on Discrete Algorithms (1990), 12--21.

....K. 2 Checking whether K is satisfiable therefore amounts to checking whether there is a cycle with negative weight in K: this is checkable in polynomial time by Floyd s or Ford s shortest path algorithm (see [McH90] Chapter 3) there are even efficient incremental algorithms to do this [AIMSN90] It is easy to check that any constraint set produced by the tableau rules from the initial tableau T 0 is well formed. ltl1.tex Peter H. Schmitt, Jean Goubault Larrecq DRAFT Do not distribute 8 So, as a last rule we introduce the constraint rule which declares a branch (B; K) closed (put ....

G. Ausiello, G. F. Italiano, A. Marchetti Spaccamela, and U. Nanni. Incremental algorithms for minimal length paths. In Proc. 1st ACM-SIAM Symposium on Discrete Algorithms, pages 12--21, 1990.

....to changes in the input data. Domains for such algorithms have included: ffl graph theoretic algorithms: connectivity [ES81, Har83, Che84] spanning trees [SP73, CH78, FS84, Fre85] spanning forests [Wes89] shortest paths [Rod68, Che76, GSV78, Fuj81, CC82, Gaz83, EG85, AMSN89, AIMSN90, Ita91] biconnected components [Sac86, WT92, BT90] triconnected components [Ita91, BT90] transitive closure [IK83, Ita86, Ita88, LPv88, YS88, Yel91] planar graphs [Tam88, TP90, BT89, EIT 92, PT88] ffl computational geometry [Ov81, CBT 92] ffl data bases [ABJ89] ffl ....

G. Ausiello, G. F. Italiano, A. Marchetti-Spaccamela, and U. Nanni. Incremental algorithms for minimal length paths. In Proceedings of the First Annual ACM-SIAM Symposium on Discrete Algorithms, pages 12--21. Society for Industrial and Applied Mathematics, 1990.

....of the query. The best known semidynamic data structures supporting insertions in digraphs with unit edge lengths use O(n 2 ) space and have constant query time; the total time to process all edge insertions is O(n 3 log n) which amortizes to O(n log n) time per insertion for dense graphs [6,73]. 2.5 Minimum Spanning Tree A spanning tree of a connected graph G is an edge induced subgraph T of G such that T is a tree and every vertex of G is in T . If G is not connected then the spanning trees of each connected component form a spanning forest. If the edges of G are weighted, then a ....

G. Ausiello, G.F. Italiano, A. Marchetti-Spaccamela, and U. Nanni, "Incremental Algorithms for Minimal Length Paths," Proc. ACM-SIAM Symp. on Discrete Algorithms (1990), 12--21.

....structure quickly. In other words a small change to the input graph should not force us to recompute the entire data structure. Thus the challenge of constructing a dynamic data structure is to satisfy both these requirements simultaneously. Though there are many algorithms for the dynamic problem [7,27,33] (see also [24] none of them can simultaneously handle both updates and queries in time that is sublinear in the input size. 1.1.3 Finding shortest paths in parallel and dynamic settings In this thesis we give efficient exact and approximate algorithms for solving shortestpath problems in ....

....for fully dynamic data structures to various graph problems. See [81] for a complexity theoretic approach to dynamic computation. As we discussed in Chapter 1 the shortest path problem is not very well understood in the dynamic realm. Though there are many algorithms for the dynamic problem [7, 24,27,33], none of them can simultaneously handle both updates and queries in time that is sublinear in the input size. We say that a path is an ffl approximate shortest path if its length is at most 1 ffl times the distance between its endpoints. In this chapter we show that if we are willing to settle ....

G. Ausiello, G.F. Italiano, A. Marchetti-Spaccamela, and U. Nanni, "Incremental algorithms for minimal length paths," Proc. ACM-SIAM Symp. on Discrete Algorithms (1990), 12--21.

.... of the absolute values of the edge lengths is D, then the time per operation is O(n 9=7 log D) worst case for queries, edge deletion, and length changes, and amortized for edge insertion) the space requirement is O(n) Several types of partially dynamic algorithms for shortest paths appear in [AuItMaNa90 ], EvGa85] FrMaNa94] and [Ro85] Although it is one of the most important dynamic graph algorithms problems, there is less known about shortest paths than about many other problems, and this is an important topic for future study. In a recent breakthrough, Henzinger and King [HeKi95] obtained ....

G. Ausiello, G. Italiano, A. Marchetti-Spaccamela, and U. Nanni, Incremental Algorithms for Minimal Length Paths, Journal of Algorithms, 12 (1991), pp. 615--638.

.... discussed by various authors, such as Even Shiloach [4] and Ibaraki Katoh [8] transitive closures) La Poutr e van Leeuwen [11] transitive closures and reductions) Frederickson [6] minimum spanning trees) and Goto Sangiovanni Vincentelli [7] Rohnert [14] Even Gazit [3] and Ausiello et al. [2] (least cost paths) Our problem can be formalized as follows: given a digraph G = V; E) and a cost function C : E IR, which does not imply negative cost cycles, we want to compute LeastCost(v; ffi ) the cost of the least cost path from a given origin r to the node v when the cost of each ....

G.Ausiello et al. Incremental Algorithms for Minimal Length Paths. ACM-SIAM, Symp. on Discrete Algorithms (1990).

.... deletion or edge cost increase (m being the current number of edges in the graph) Note that the update time after an edge deletion or edge cost increase is equal to the time required to recompute all pairs shortest paths from scratch [22] Improvements on these algorithms have been achieved in [4] with respect to the worstcase complexity of a sequence of edge insertions or edge cost decreases (thus providing a better bound per update in the amortized sense) in the special case where the edge costs are nonnegative integers. More specifically, the data structure in [4] can be updated in ....

....have been achieved in [4] with respect to the worstcase complexity of a sequence of edge insertions or edge cost decreases (thus providing a better bound per update in the amortized sense) in the special case where the edge costs are nonnegative integers. More specifically, the data structure in [4] can be updated in O(Cn 3 log(nC) time after a sequence of at most O(n 2 ) edge insertions or at most O(Cn 2 ) edge cost decreases, where C is the largest value of an edge cost. Edge deletions or edge cost increases are not considered in [4] For the important case of planar digraphs ....

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G. Ausiello, G.F. Italiano, A.M. Spaccamela, U. Nanni, Incremental algorithms for minimal length paths, J. of Algorithms, 12 (1991), 615-638.

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G. Ausiello, G. F. Italiano, A. Marchetti Spaccamela, and U. Nanni. Incremental algorithms for minimal length paths. Journal of Algorithms, 12(4):615--638, 1991.

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G. Ausiello, G. F. Italiano, A. Marchetti-Spaccamela and U. Nanni. Incremental algorithms for minimal length paths. Journal of Algorithms, 12, 4 (1991), 615-638.

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G. Ausiello, G.F. Italiano, A. Marchetti-Spaccamela, and U. Nanni. Incremental algorithms for minimal length paths. Journal of Algorithms, 12(4):615--38, 1991.

....worst case analysis. Furthermore we consider an intermediate model between worst case analysis and average case analysis: the semi random adversary introduced in [3] 1 Introduction Significant progress has been recently made in the design of algorithms and data structures for dynamic graphs [1, 5, 6, 8, 11, 12, 13, 16, 17, 18, 19, 20, 21, 24]. These data structures support insertions and deletions of edges and or nodes in a graph, in addition to several types of queries. The goal is to compute the new solution in the modified graph without having to recompute it from scratch. Usually, the sequence of insertions deletions of edges is ....

G.Ausiello, G.F.Italiano, A.Marchetti-Spaccamela, U.Nanni, Incremental algorithms for minimal length paths, J. of Algorithms, 12 , 615-638, 1991.

....9, 10, 17, 18, 20] but their running times in the worst case were comparable to recomputing APSP from scratch. The rst dynamic shortest path algorithms which are provably faster than recomputing APSP from scratch, only worked on graphs with small integer weights. In particular, Ausiello et al. [1] proposed a decrease only shortest path algorithm for directed graphs having positive integer weights less than C: the amortized running time of their algorithm is O(Cn log n) per edge insertion. Henzinger et al. 12] designed a fully dynamic algorithm for APSP on planar graphs with integer ....

G. Ausiello, G.F. Italiano, A. Marchetti-Spaccamela, and U. Nanni. Incremental algorithms for minimal length paths. Journal of Algorithms, 12(4):615-38, 1991.

....times of output bounded dynamic algorithms are comparable to recomputing APSP from scratch. There seem to be few dynamic shortest path algorithms which are provably faster than recomputing APSP from scratch, and they only work on graphs with small integer weights. In particular, Ausiello et al. [3] proposed an incremental shortest path algorithm for directed graphs having positive integer weights less than C: the amortized running time of their algorithm is O(Cn log n) per edge insertion. Henzinger et al. 22] designed a fully dynamic algorithm for APSP on planar graphs with integer ....

G. Ausiello, G.F. Italiano, A. Marchetti-Spaccamela, and U. Nanni. Incremental algorithms for minimal length paths. Journal of Algorithms, 12(4):615--38, 1991.

....times of output bounded dynamic algorithms are comparable to recomputing APSP from scratch. There seem to be few dynamic shortest path algorithms which are provably faster than recomputing APSP from scratch, and they only work on graphs with small integer weights. In particular, Ausiello et al. [3] proposed an incremental shortest path algorithm for directed graphs having positive integer weights less than C: the amortized running time of their algorithm is O(Cn log n) per edge insertion. Henzinger et al. 13] designed a fully dynamic algorithm for APSP on planar graphs with integer ....

G. Ausiello, G.F. Italiano, A. Marchetti-Spaccamela, and U. Nanni. Incremental algorithms for minimal length paths. Journal of Algorithms, 12(4):615-38, 1991.

....interest in dynamic problems on graphs. In particular, much attention has been devoted to the dynamic maintenance of connected components [14, 16, 43] and higher connectivity [8, 10, 18, 19, 20, 21, 32, 35, 53] transitive closure [29, 30, 31, 37, 47, 55] planarity [7, 8, 46] shortest paths [2, 5, 13, 39, 44], and minimum spanning trees [10, 11, 16] In these problems one would like to answer queries on graphs that are undergoing a sequence of updates, such as insertions and deletions of edges and vertices. The goal of a dynamic graph algorithm is to update efficiently the solution of a problem after ....

G. Ausiello, G. F. Italiano, A. Marchetti-Spaccamela, and U. Nanni. Incremental algorithms for minimal length paths. J. Algorithms, 12:615--638, 1991.

.... algorithms [13] On the other hand, the development of fully dynamic algorithms for maintenance of various properties on directed graphs (digraphs) turned out to be a much harder problem and much of the research so far was concentrated on the design of partially dynamic algorithms (see e.g. [4, 7, 8, 11, 26, 27, 28, 32]) Only recently, fully dynamic algorithms have started to appear for maintenance of shortest path trees [18, 19, 30] and transitive closure [9, 23, 24, 25] However, despite the number of interesting theoretical results achieved, very little has been done so far with respect to implementations ....

G. Ausiello, G.F. Italiano, A. Marchetti-Spaccamela, and U. Nanni. Incremental algorithms for minimal length paths. Journal of Algorithms, 12:615-638, 1991.

.... e Sistemistica, Universit a di Roma La Sapienza , Via Salaria 113 00198 Roma, Italy, ffrigioni,ioffreda,nanni,pasqualog dis.uniroma1.it 1 1 Introduction A lot of efforts have been done in the last years in order to devise efficient algorithms for dynamic graph problems (e.g. see [6, 9, 13, 14, 15, 16, 18, 20, 23, 24, 25, 26, 30, 31, 32]) motivated by theoretical as well as practical applications. In the literature, the most used dynamic model is the following: we are given a graph G and we want to answer queries on a property P of G, while the graph is changing due to insertions and deletions of edges. For instance, if the ....

....paper we provide the first experimental study of dynamic algorithms for the single source shortest paths problem. 1. 1 Previous theoretical results Many dynamic solutions have been proposed in the literature for the shortest paths problem, both for the single source and the all pairs versions [6, 9, 14, 15, 16, 18, 20, 26, 31, 32]. A fully dynamic solution for maintaining all pairs shortest paths on planar graphs with unrestricted edge weights is given in [26] but the algorithm is complex and far from being practical. In [9] efficient dynamic solutions are provided for graphs with bounded treewidth when the weights of ....

[Article contains additional citation context not shown here]

G. Ausiello, G. F. Italiano, A. Marchetti-Spaccamela, and U. Nanni. Incremental algorithms for minimal length paths. Journal of Algorithms, 12(4):615--638, 1991.

....allowed we refer to the fully dynamic problem; if we consider only insertions (deletions) of arcs then we refer to the incremental (decremental) problem. In the case of positive arc weights there is a number of papers that propose different solutions to deal with dynamic shortest paths problems [3, 4, 7, 8, 10, 11, 13, 17, 18]. However, in the general case, neither a fully dynamic solution nor a decremental solution for the single source shortest path problem is known in the literature that is asymptotically better than recomputing the new solution from scratch. Work partially supported by the ESPRIT Long Term ....

G. Ausiello, G. F. Italiano, A. Marchetti-Spaccamela and U. Nanni. Incremental algorithms for minimal length paths. Journal of Algorithms, 12, 4 (1991), 615--638.

No context found.

G. Ausiello, G. F. Italiano, A. Marchetti-Spaccamela, and U. Nanni. Incremental algorithms for minimal length paths. Journal of Algorithms, 12:615--638, 1991.

....complex and far from being practical. In [4] the authors consider efficient dynamic solutions for graphs with bounded treewidth when the weight of edges might change, but without considering insertions and deletions of edges. An efficient solution for the incremental problem has been proposed in [3] assuming that edge weights are integers restricted in the range [1: C] Further results concerning the dynamic shortest paths problem for general graphs have been proposed, for example, in [7, 18, 19] To the best of our knowledge, if insertions and deletions of edges are allowed and there is no ....

G. Ausiello, G. F. Italiano, A. Marchetti-Spaccamela and U. Nanni, Incremental Algorithms for Minimal Length Paths, J. Algorithms, 12, 4 (1991), 615--638.

....Grant CDA 9024735. z University of Venice Ca Foscari , Venice, Italy. Supported in part by the ESPRIT LTR Project no. 20244 (ALCOM IT) and by a Research Grant from University of Venice Ca Foscari . Most of the efficient data structures available for directed graphs are partially dynamic [2, 13, 29, 30, 31, 37, 39, 43, 53], and only preliminary results are available for fully dynamic problems [25] For this reason, an alternative viewpoint that has been proposed is to measure the complexity of a dynamic algorithm as a function of the output change [17, 40] The main dynamic problems considered on directed graphs ....

G. Ausiello, G. F. Italiano, A. Marchetti Spaccamela, and U. Nanni. Incremental algorithms for minimal length paths. J. Algorithms, 12:615--638, 1991.

....has been focusing on dynamic graph algorithms and the design of algorithmic techniques for sequential problems. Shortest paths and reachability. In this area, new dynamic shortest paths algorithms have been proposed and analyzed both from the viewpoint of average case and worst case complexity [50, 49]. In [218] algorithms for dynamically maintaining single source shortest paths in planar graphs are presented, as well as for a static version of the all pairs shortest path problems where the queries refer to a subset of all the possible queries. Other results on the single source shortest path ....

G. Ausiello, G. F. Italiano, A. Marchetti Spaccamela, and U. Nanni. Incremental algorithms for minimal length paths. J. Algorithms, 12(4):615--638, 1991.

....real world. 1. Introduction In this paper we deal with the dynamic single source shortest path problem on directed graphs with positive real edge weights from an experimental point of view. A great interest has been devoted in the last years to the solution of dynamic graph problems (e.g. see [4, 8, 10, 12, 13, 15]) motivated by theoretical as well as practical applications. In the literature, the most used dynamic model is the following: we are given a graph G and we want to answer queries on a property P of G, while the graph is changing due to insertions and deletions of edges. If the graph represents a ....

.... formatting, routing in communication systems, robotics (see e.g. 1] for a wide variety of application settings for the shortest paths problem) Many solutions have been proposed in the literature to deal with dynamic shortest paths problems both for the single source and the all pairs versions [4, 9, 12, 13, 15]. In the case of planar graphs a fully dynamic solution for maintaining all pairs shortest paths with unrestricted edge weights has been proposed in [13] but the proposed algorithm is complex and far from being practical. An efficient solution for the all pairs incremental problem has been ....

[Article contains additional citation context not shown here]

G. Ausiello, G. F. Italiano, A. Marchetti-Spaccamela, U. Nanni, Incremental Algorithms for Minimal Length Paths, J. of Algorithms 12 (4), (1991), 615--638.

....with updates on the structure of the graph, while maintaining the possibility to answer queries on shortest paths without recomputing them from scratch. Various approaches have been considered in literature to deal with dynamic shortest path problems both for single source and all pairs versions [4, 7, 8, 13, 14, 18, 20], providing several noncomparable solutions, each characterized by a given setting for (a) the kind of considered graph and edge weights, b) the set of allowed updates on the structure of the graph, and (c) the adopted measure of performances. Some of the proposed solutions pursue a trade off ....

....These solutions use a topological partition of the graph based on a recursive application of the planar separator theorem [15] all these algorithms are complex and far from being practical. The explicit update of all pairs shortest paths for general graphs has been considered, for example, in [4, 7, 20]. In the particular case of edge insertions in a directed graph G = V; E) with jV j = n, and jEj = m, and integer edge weights in the range [0: C] an algorithm is provided in [4] requiring O(Cn log n) amortized time per edge insertion in any sequence of Omega Gamma m) insertions, while ....

[Article contains additional citation context not shown here]

G. Ausiello, G. F. Italiano, A. Marchetti-Spaccamela, and U. Nanni, Incremental Algorithms for Minimal Length Paths, Journal of Algorithms, 12, 4 (1991), 615--638.

.... problems [11] Moreover, despite intensive research on dynamic problems on graphs (such as dynamic maintenance of connectivity [7, 8, 10, 11, 14, 20, 22, 29, 30] 2 and 3 connectivity [7, 12, 29, 30] transitive closure [3, 4, 15, 16, 17, 18, 19, 31] planar graphs [6, 7, 19, 25] shortest paths [2, 9, 21, 24, 31] and minimum spanning trees [5, 8, 11, 24] there are very few graphtheoretic problems for which a fully dynamic non trivial algorithm is known. As mentioned in [30] the fully dynamic maintenance of the connected components of a graph differs substantially from the fully dynamic maintenance of ....

G. Ausiello, G. F. Italiano, A. Marchetti-Spaccamela, U. Nanni, "Incremental algorithms for minimal length paths", J. Algorithms , to appear.

....tree it belongs to. Dynamic problems on graphs have been extensively studied. Several algorithms have been proposed for maintaining fundamental structural information about dynamic graphs, such as connectivity [9, 10, 15, 24, 26] transitive closure [17, 18, 19, 20, 21, 34, 23] and shortest paths [1, 8, 25, 28, 34]. Dynamic planar graphs arise in communication networks, graphics, and VLSI design, and they occur in algorithms that build planar subdivisions such as Voronoi diagrams. Algorithms have been proposed for maintaining the embedding of a planar graph [29] and for incremental planarity testing [2, 3] ....

G. Ausiello, G. F. Italiano, A. M. Spaccamela, and U. Nanni. Incremental algorithms for minimal length paths. In Proc. 1st ACM-SIAM Symp. on Discrete Algorithms, pages 12--21, 1990.

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G. Ausiello, G.F. Italiano, A. Marchetti-Spaccamela, and U. Nanni, "Incremental Algorithms for Minimal Length Paths," Proc. ACM-SIAM Symp. on Discrete Algorithms (1990), 12--21.

No context found.

G. Ausiello, G.F. Italiano, A. Marchetti-Spaccamela, and U. Nanni. Incremental algorithms for minimal length paths. J. Algorithms, 12(4):615--638, 1991.

No context found.

Ausiello, G., G. F. Italiano, A. Marchetti-Spaccamela and U. Nanni, Incremental algorithms for minimal length paths, Journal of Algorithms 12 (1991), pp. 615--638.

No context found.

Ausiello, G., Italiano, G.F., Spaccamela, A.M., and Nanni, U., "Incremental algorithms for minimal length paths," pp. 12-21 in Proceedings of the First Annual ACM-SIAM Symposium on Discrete Algorithms, (San Francisco, CA, Jan. 22-24, 1990), Society for Industrial and Applied Mathematics, Philadelphia, PA (1990).

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Ausiello, G., Italiano, G.F., Spaccamela, A.M., and Nanni, U., "Incremental algorithms for minimal length paths," Journal of Algorithms, (12) pp. 615-638 (1991).

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Ausiello, G., Italiano, G.F., Spaccamela, A.M., and Nanni, U., "Incremental algorithms for minimal length paths," pp. 12-21 in Proceedings of the First Annual ACM-SIAM Symposium on Discrete Algorithms, (San Francisco, CA, Jan. 22-24, 1990), Society for Industrial and Applied Mathematics, Philadelphia, PA (1990).

No context found.

Ausiello, G., Italiano, G.F., Spaccamela, A.M., and Nanni, U., "Incremental algorithms for minimal length paths," Journal of Algorithms, (12) pp. 615-638 (1991).

No context found.

Ausiello, G., Italiano, G.F., Spaccamela, A.M., and Nanni, U., "Incremental algorithms for minimal length paths," pp. 12-21 in Proceedings of the First Annual ACM-SIAM Symposium on Discrete Algorithms, (San Francisco, CA, Jan. 22-24, 1990), Society for Industrial and Applied Mathematics, Philadelphia, PA (1990).

No context found.

G. Ausiello, G.F. Italiano, A.M. Spaccamela, U. Nanni. Incremental Algorithms for Minimal Length Paths. Journal of Algorithms, 12(4): 615638, 1990.

No context found.

G. Italiano, A. Marchetti-Spaccamela, U. Nanni, \Incremental Algorithms for Minimal Length Paths," Journal of Algorithms, vol. 12, 1991, p. 615-638.

No context found.

G. Italiano, A. Marchetti-Spaccamela, U. Nanni, "Incremental Algorithms for Minimal Length Paths," Journal of Algorithms, vol. 12, 1991, p. 615-638.

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