V. Y. Pan and J. H. Reif. The parallel computation of minimum cost paths in graphs by stream contraction. Information Processing Letters 40, 79-83, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the only algorithm admitting sufficiently accurate NC implementations is Newton s iterative method, and the word size required to guarantee worst case correctness appears to be the critical Istituto di Matematica Computazionale, Consiglio Nazionale delle Ricerche, Via S. Maria 46, 56126 Pisa, Italy. Facolt a di Economia di Foggia, Universit a di Bari, Via IV Novembre 1, 71100 Foggia, Italy, and IMC CNR, 56126 Pisa, Italy. Dept. of Computer Science, Brown University, Providence, Rhode Island 02912. Supported in part by NSF Grant CCR94 00232. complexity measure. Our ....

....required to guarantee worst case correctness appears to be the critical Istituto di Matematica Computazionale, Consiglio Nazionale delle Ricerche, Via S. Maria 46, 56126 Pisa, Italy. Facolt a di Economia di Foggia, Universit a di Bari, Via IV Novembre 1, 71100 Foggia, Italy, and IMC CNR, 56126 Pisa, Italy. Dept. of Computer Science, Brown University, Providence, Rhode Island 02912. Supported in part by NSF Grant CCR94 00232. complexity measure. Our analysis also accounts for the observed instability of the considered superfast methods when implemented with the same floating point ....

[Article contains additional citation context not shown here]

Pan, V. and Reif, J. H., The Parallel Computation of the Minimum Cost Paths in Graphs by Stream Contraction, Inform. Proc. Letters 40 (1991), 79--83.

....algorithm that takes time O(n 4=3 log nL) where the lengths are integers greater than GammaL. For general graphs, the best bound known is O(n 1=2 m log L) time, due to Goldberg [14] which yields O(n 3=2 log L) time on sparse (e.g. planar) graphs. For undirected planar graphs, Pan and Reif [25,26] showed how to achieve O(n 3=2 ) time using separators. Cohen [4] showed how to achieve the same bound for directed planar graphs. Previously no algorithm handling negative lengths was known that ran faster than O(n 3=2 ) Our algorithm overcomes this apparent barrier, improving the time by a ....

....nodes of R, each edge of GR corresponds to a path in R, and 1. jE(GR )j = jE(R)j log(jE(R)j) 2. for any pair of nodes u; v 2 R there exists a shortest u to v path in GR that has size O(log jV (R)j) This is done using a straightforward divide andconquer. The time required is O(r 3=2 ) time [4,25,26], but for ease of exposition we describe a slightly simplified version that requires a log factor more time. Given a graph R with splitting set S, we proceed as follows. Suppose R has r nodes. Let X be a size O( p r) separator for R that breaks R into up to three pieces R 1 ; R 2 ; R 3 such that ....

[Article contains additional citation context not shown here]

V. Pan and J. H. Reif, "The parallel computation of minimum cost paths in graphs by stream contraction, " Information Processing Letters 40 (1991), 79-- 83.

....directed acyclic graph with exactly one source and exactly one sink, such that the graph can be constructed by series and parallel compositions. Series parallel digraphs are a special case of planar st graphs. There are also parallel graph algorithms for single source shortest paths. Pan and Reif [25, 26] developed an O(log 3 n) time, O(n 1:5 ) work algorithm for single source shortest paths in planar undirected graphs, and this result has been generalized to planar directed graphs [5, 11] Klein and Subramanian [21] gave a linear processor, polylog time algorithm for single source shortest ....

V. Pan and J. H. Reif, "The parallel computation of minimum cost paths in graphs by stream contraction, " Information Processing Letters, 40 (1991), pp. 79--83.

....p n) node separators 1 can be found efficiently in polylog time, including constant genus graphs and two dimensional geometric overlap graphs. 2 The best previously known polylog time algorithm for single source shortest paths in undirected graphs with such separators is that of Pan and Reif [25,26], which does O(n 1:5 ) work. Cohen [4] has given an algorithm with similar bounds for the directed case. The previous bounds are no better for breadth first search, the special case where every edge length is one. Our shortest path algorithm applied to planar graphs in particular has several ....

V. Pan and J. H. Reif, "The parallel computation of minimum cost paths in graphs by stream contraction," Information Processing Letters 40 (1991), 79--83.

....algorithm to find single source shortest paths in constant genus graphs if we are given as part of the input a separator decomposition tree of the underlying graph. The best previously known polylog time algorithm for single source shortest paths in planar undirected graphs is that of Pan and Reif [82,83], which does O(n 1:5 ) work. Cohen [14] has given an algorithm with similar bounds for the directed case. The previous bounds are no better for breadth first search, the special case where every edge length is one. Our shortest path algorithm applied to planar graphs in particular has several ....

....algorithm that takes time O(n 4=3 log(nL) where the lengths are integers greater than GammaL. For general graphs, the best bound known is O(n 1=2 m log L) time, due to Goldberg [44] which yields O(n 3=2 log L) time on sparse (e.g. planar) graphs. For undirected planar graphs, Pan and Reif [82,83] showed how to achieve O(n 3=2 ) time using separators. Cohen [14] showed how to achieve the same bound for directed planar graphs. Previously no algorithm handling negative lengths was known that ran faster than O(n 3=2 ) Our algorithm overcomes this apparent barrier, improving the time by a ....

[Article contains additional citation context not shown here]

V. Pan and J. H. Reif, "The parallel computation of minimum cost paths in graphs by stream contraction," Information Processing Letters 40 (1991), 79--83.

No context found.

V. Y. Pan and J. H. Reif. The parallel computation of minimum cost paths in graphs by stream contraction. Information Processing Letters 40, 79-83, 1991.

....with n M(s(n) processors. Gazit and Miller [31] gave bounds of parallel time n log log n) with n M(s(n) processors and Armon and Reif [3] decreased this parallel time to O(log n) with n M(s(n) 1 # processors, for # 0. Stream Contraction is a technique developed by Pan and Reif [72] to decrease the time to solve combinatorial matrix problems over semirings; the stream contraction method decreased the parallel time by a logarithmic factor without a processor penalty. 1.5. Dense Structured Matrices There is a large body of work on sequential algorithms which reduce the ....

....a recursive factorization (RF) of an SPD matrix, using the techniques of Newton s iteration and Newton Hensel lifting, as well as the Variable Diagonal technique. We provide improvements to these techniques by application of a generalization of the stream contraction technique of Pan and Reif [72] to do a multilevel, pipelined Newton iteration, followed by multilevel, pipelined Newton Hensel lifting. Our algorithms give an exact factorization, but nevertheless avoid computation of the characteristic polynomial or related forms. Using reductions to the recursive factorization algorithm, we ....

[Article contains additional citation context not shown here]

V. Pan and J.H.Reif, The Parallel Computation of Minimum Cost Paths in Graphs by Stream Contraction, Information Proc. Lett., 40, (1991), pp. 79-83.

....Reif presented BFS algorithms for planar graphs [PR 89] Their idea was to solve the minimal path problem independently in each separated subgraph, and then to union the solutions. The first version of their algorithm required O(log 2 (n) time using n 1:5 processors. In the later 6 version [PR 91] they used a method called parallel stream contraction to speed up the calculation to O(log(n) time using the same number of processors by beginning to calculate the minimal distances between separators in level i before the calculations from level i 1 are complete. Assume that the last level ....

....that the last level of separators is L log 3 2 (n) In every iteration i they find minimal paths that use 2 i j GammaL or fewer edges between the vertices of all the separators in every level j. This yields an O(log(n) time complexity with the same processor bound. Lemma 2. 3 (Pan and Reif [PR 91] Given a planar graph with n vertices, there is an algorithm to compute a BFS tree in O(log(n) time with n 1:5 processors. Testing Isomorphism of planar graphs. Hopcroft and Tarjan [HT 73b] presented a sequential planar isomorphism algorithm that runs in O(n Delta log(n) time. Hopcroft and ....

[Article contains additional citation context not shown here]

V. Pan and J.H.Reif, The Parallel Computation of Minimum Cost Paths in Graphs by Stream Contraction, Information Proc. Lett., 40, (1991), pp. 79-83. 23

....for this problem. However, they either need #(n 3 log n) operations or only work for the more narrow class of the input graphs and or digraphs (which have the edge weights bounded, say, by a constant or have a family of small separators available) AGM] DNS] DS] GM] L] PK] PR1] [PR2], S] The recent algorithm of [PP1] and [PP2] uses O(log 2.5 n) parallel time and O(n 3 ) operations in the case of a general graph with n vertices. In this paper we improve the latter time bound to the new record value of O(I (n) log n) still using O(n 3 ) operations. Here I (n) is the ....

....log 7 6 n) using p processors. REMARK. Algorithms APSP1 and APSP2 sequentially evaluate the transitive closure of the matrices on the diagonal. This property is useful for reducing the complexity of computing the all pair shortest paths in graphs with a family of precomputed separators [PR1] [PR2]. 2.3. A Faster Algorithm. We divide matrix A into levels (see Figure 2) The 0th level is A (0) 0 = A. For each matrix B = A ( j ) i at level j we divide it into four submatrices of equal size, B 0,0 , B 0,1 , B 1,0 , B 1,1 , and define A ( j 1) 2i = B 0,0 and A ( j 1) 2i 1 = ....

V. Y. Pan and J. H. Reif. The parallel computation of minimum cost paths in graphs by stream contraction. Inform. Process. Lett. 40:79--83, 1991. Parallel Algorithms for Computing All Pair Shortest Paths in Directed Graphs 415

No context found.

V. Pan and J. H. Reif, The Parallel Computation of Minimum Cost Paths in Graphs by Stream Contraction, Information Proc. Lett., 40, 79-83, (1991).

.... d Gamma 1, thus avoiding the application of DFT until we compute the values of z d (x) This way, we contract the stream of recursive steps, by cutting off their slowest parts (that is, DFT s) and thus accelerating the transition to each new step (compare another example of stream contraction in [9]) As a result, the n coefficients of r(x) mod x n are computed at the cost bounded by OA (log n; n log 2 n) 5] 2 3 A Basis Algorithm for New Improvements and Its Recursive Restarting In this and in the next two sections, we will combine the two ways of applying Newton s iteration ....

V. Y. Pan and J. H. Reif, "The Parallel Computation of the Minimum Cost Paths in Graph by Stream Contraction,"Information Processing Letters, 40 (1991) 79--83.

....processor arrays [Le92] Q94] Thus, it is possible to implement our algorithms efficiently assuming the latter models. 1.4 Our main results. The algorithms of this paper extend our previous work on parallel computations with general matrices [P85] P87] P93a] BP94] cf. also [PR91], P92a] P93b] PR93] by means of incorporation of some techniques developed in [P90] P92] P92b] P93] P93a] for computations with Toeplitz and Toeplitz like matrices. As a result, we arrive at some the new RNC algorithms for the most fundamental computations with the latter classes of ....

....borrow from [P92] and [P92b] P93] P93a] respectively. The above outline was essentially given in [BP94] Presently, we also add the technique of stream contraction specified in section 10 (and, essentially, being the pipelining of the two processes of RD and Newton s iteration) borrowed from [PR91]. Stream contraction enables additional acceleration of our algorithms by factor log n. Using the technique of stream contraction for the acceleration of Toeplitz like computations was also proposed in [R95] though the algorithms of [R95] did not give any improvement of the processor bounds in ....

[Article contains additional citation context not shown here]

V. Y. Pan, J. Reif, The Parallel Computation of the Minimum Cost Paths in Graphs by Stream Contraction, Information Processing Letters, 40, 79--83, 1991.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC