Results 1  10
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7,056
Finding the k Shortest Paths
, 1997
"... We give algorithms for finding the k shortest paths (not required to be simple) connecting a pair of vertices in a digraph. Our algorithms output an implicit representation of these paths in a digraph with n vertices and m edges, in time O(m + n log n + k). We can also find the k shortest pat ..."
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Cited by 401 (2 self)
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We give algorithms for finding the k shortest paths (not required to be simple) connecting a pair of vertices in a digraph. Our algorithms output an implicit representation of these paths in a digraph with n vertices and m edges, in time O(m + n log n + k). We can also find the k shortest
A new approach to the maximum flow problem
 JOURNAL OF THE ACM
, 1988
"... All previously known efficient maximumflow algorithms work by finding augmenting paths, either one path at a time (as in the original Ford and Fulkerson algorithm) or all shortestlength augmenting paths at once (using the layered network approach of Dinic). An alternative method based on the pre ..."
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Cited by 672 (33 self)
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All previously known efficient maximumflow algorithms work by finding augmenting paths, either one path at a time (as in the original Ford and Fulkerson algorithm) or all shortestlength augmenting paths at once (using the layered network approach of Dinic). An alternative method based
Theoretical improvements in algorithmic efficiency for network flow problems

, 1972
"... This paper presents new algorithms for the maximum flow problem, the Hitchcock transportation problem, and the general minimumcost flow problem. Upper bounds on ... the numbers of steps in these algorithms are derived, and are shown to compale favorably with upper bounds on the numbers of steps req ..."
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Cited by 560 (0 self)
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problem, in which all shortestpath computations are performed on networks with all weights nonnegative. In particular, this
Fibonacci Heaps and Their Uses in Improved Network optimization algorithms
, 1987
"... In this paper we develop a new data structure for implementing heaps (priority queues). Our structure, Fibonacci heaps (abbreviated Fheaps), extends the binomial queues proposed by Vuillemin and studied further by Brown. Fheaps support arbitrary deletion from an nitem heap in qlogn) amortized tim ..."
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Cited by 739 (18 self)
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in the problem graph: ( 1) O(n log n + m) for the singlesource shortest path problem with nonnegative edge lengths, improved from O(m logfmh+2)n); (2) O(n*log n + nm) for the allpairs shortest path problem, improved from O(nm lo&,,,+2,n); (3) O(n*logn + nm) for the assignment problem (weighted bipartite
GPSR: Greedy perimeter stateless routing for wireless networks
 MOBICOM
, 2000
"... We present Greedy Perimeter Stateless Routing (GPSR), a novel routing protocol for wireless datagram networks that uses the positions of touters and a packer's destination to make packet forwarding decisions. GPSR makes greedy forwarding decisions using only information about a router's i ..."
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Cited by 2290 (8 self)
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's immediate neighbors in the network topology. When a packet reaches a region where greedy forwarding is impossible, the algorithm recovers by routing around the perimeter of the region. By keeping state only about the local topology, GPSR scales better in perrouter state than shortestpath and ad
AllPairs Shortest Paths for Unweighted Undirected Graphs in o(mn) Time
 Proc. ACMSIAM Symposium on Discrete Algorithms (SODA
, 2006
"... Abstract We revisit the allpairsshortestpaths problem for an unweighted undirected graph with n vertices and m edges. We present new algorithms with the following running times: O(mn = log n) if m? n log ..."
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Cited by 23 (1 self)
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Abstract We revisit the allpairsshortestpaths problem for an unweighted undirected graph with n vertices and m edges. We present new algorithms with the following running times: O(mn = log n) if m? n log
Internet traffic engineering by optimizing OSPF weights
 in Proc. IEEE INFOCOM
, 2000
"... Abstractâ€”Open Shortest Path First (OSPF) is the most commonly used intradomain internet routing protocol. Traffic flow is routed along shortest paths, splitting flow at nodes where several outgoing links are on shortest paths to the destination. The weights of the links, and thereby the shortest pa ..."
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Cited by 403 (13 self)
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Abstractâ€”Open Shortest Path First (OSPF) is the most commonly used intradomain internet routing protocol. Traffic flow is routed along shortest paths, splitting flow at nodes where several outgoing links are on shortest paths to the destination. The weights of the links, and thereby the shortest
A general approximation technique for constrained forest problems
 SIAM J. COMPUT.
, 1995
"... We present a general approximation technique for a large class of graph problems. Our technique mostly applies to problems of covering, at minimum cost, the vertices of a graph with trees, cycles, or paths satisfying certain requirements. In particular, many basic combinatorial optimization proble ..."
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Cited by 414 (21 self)
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problems fit in this framework, including the shortest path, minimumcost spanning tree, minimumweight perfect matching, traveling salesman, and Steiner tree problems. Our technique produces approximation algorithms that run in O(n log n) time and come within a factor of 2 of optimal for most
An optimal algorithm to solve the allpairs shortest paths on unweighted interval graphs
 Networks
, 1992
"... We present an O(n2) timeoptimal algorithm for solving the unweighted allpair shortest path problem on interval graphs, an important subclass of perfect graphs. An interesting structure called the neighborhood tree is studied and used in the algorithm. This tree is formed by identifying the success ..."
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Cited by 7 (0 self)
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We present an O(n2) timeoptimal algorithm for solving the unweighted allpair shortest path problem on interval graphs, an important subclass of perfect graphs. An interesting structure called the neighborhood tree is studied and used in the algorithm. This tree is formed by identifying
On dynamic shortest paths problems
, 2004
"... We obtain the following results related to dynamic versions of the shortestpaths problem: (i) Reductions that show that the incremental and decremental singlesource shortestpaths problems, for weighted directed or undirected graphs, are, in a strong sense, at least as hard as the static allpairs ..."
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Cited by 41 (2 self)
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pairs shortestpaths problem. We also obtain slightly weaker results for the corresponding unweighted problems. (ii) A randomized fullydynamic algorithm for the allpairs shortestpaths problem in directed unweighted graphs with an amortized update time of ~O(mpn) and a worst case query time is O(n3/4). (iii) A
Results 1  10
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7,056