Results 1  10
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19
The directed planar reachability problem
 In Proc. 25th annual Conference on Foundations of Software Technology and Theoretical Computer Science (FST&TCS), number 1373 in Lecture Notes in Computer Science
, 2005
"... Abstract. We investigate the stconnectivity problem for directed planar graphs, which is hard for L and is contained in NL but is not known to be complete. We show that this problem is logspacereducible to its complement, and we show that the problem of searching graphs of genus 1 reduces to the ..."
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Cited by 18 (7 self)
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Abstract. We investigate the stconnectivity problem for directed planar graphs, which is hard for L and is contained in NL but is not known to be complete. We show that this problem is logspacereducible to its complement, and we show that the problem of searching graphs of genus 1 reduces to the planar case. We also consider a previouslystudied subclass of planar graphs known as grid graphs. We show that the directed planar stconnectivity problem reduces to the reachability problem for directed grid graphs. A special case of the gridgraph reachability problem where no edges are directed from right to left is known as the “acyclic grid graph reachability problem”. We show that this problem lies in the complexity class UL. 1
Directed planar reachability is in unambiguous logspace
 In Proceedings of IEEE Conference on Computational Complexity CCC
, 2007
"... We show that the stconnectivity problem for directed planar graphs can be decided in unambiguous logarithmic space. 1. ..."
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Cited by 15 (4 self)
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We show that the stconnectivity problem for directed planar graphs can be decided in unambiguous logarithmic space. 1.
Evaluating monotone circuits on cylinders, planes, and torii
 In Proc. 23rd Symposium on Theoretical Aspects of Computing (STACS), Lecture Notes in Computer Science
, 2006
"... Abstract. We revisit monotone planar circuits MPCVP, with special attention to circuits with cylindrical embeddings. MPCVP is known to be in NC 3 in general, and in LogDCFL for the special case of upward stratified circuits. We characterize cylindricality, which is stronger than planarity but strict ..."
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Cited by 10 (2 self)
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Abstract. We revisit monotone planar circuits MPCVP, with special attention to circuits with cylindrical embeddings. MPCVP is known to be in NC 3 in general, and in LogDCFL for the special case of upward stratified circuits. We characterize cylindricality, which is stronger than planarity but strictly generalizes upward planarity, and make the characterization partially constructive. We use this construction, and four key reduction lemmas, to obtain several improvements. We show that monotone circuits with embeddings that are stratified cylindrical, cylindrical, planar oneinputface and focused can be evaluated in LogDCFL, AC 1 (LogDCFL), LogCFL and AC 1 (LogDCFL) respectively. We note that the NC 3 algorithm for general MPCVP is in AC 1 (LogCFL) =SAC 2.Finally, we show that monotone circuits with toroidal embeddings can, given such an embedding, be evaluated in NC. 1
A new NCalgorithm for finding a perfect matching in bipartite planar and small genus graphs (Extended Abstract)
, 2000
"... It has been known for a long time now that the problem of counting the number of perfect matchings in a planar graph is in NC. This result is based on the notion of a pfaffian orientation of a graph. (Recently, Galluccio and Loebl [7] gave a Ptime algorithm for the case of graphs of small genus.) H ..."
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Cited by 8 (2 self)
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It has been known for a long time now that the problem of counting the number of perfect matchings in a planar graph is in NC. This result is based on the notion of a pfaffian orientation of a graph. (Recently, Galluccio and Loebl [7] gave a Ptime algorithm for the case of graphs of small genus.) However, it is not known if the corresponding search problem, that of finding one perfect matching in a planar graph, is in NC. This situation is intriguing as it seems to contradict our intuition that search should be easier than counting. For the case of planar bipartite graphs, Miller and Naor [22] showed that a perfect matching can indeed be found using an NC algorithm. We present a very different NCalgorithm for this problem. Unlike the Miller...
THE ISOMORPHISM PROBLEM FOR PLANAR 3CONNECTED GRAPHS IS IN UNAMBIGUOUS LOGSPACE
, 2008
"... The isomorphism problem for planar graphs is known to be efficiently solvable. For planar 3connected graphs, the isomorphism problem can be solved by efficient parallel algorithms, it is in the class AC¹. In this paper we improve the upper bound for planar 3connected graphs to unambiguous logspace ..."
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Cited by 8 (2 self)
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The isomorphism problem for planar graphs is known to be efficiently solvable. For planar 3connected graphs, the isomorphism problem can be solved by efficient parallel algorithms, it is in the class AC¹. In this paper we improve the upper bound for planar 3connected graphs to unambiguous logspace, in fact to UL ∩ coUL. As a consequence of our method we get that the isomorphism problem for oriented graphs is in NL. We also show that the problems are hard for L.
Planar graph isomorphism is in logspace
 In IEEE Conference on Computational Complexity
, 2009
"... Abstract. We show that the isomorphism of 3connected planar graphs can be decided in deterministic logspace. This improves the previously known bound UL ∩ coUL of [13]. 1 ..."
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Cited by 8 (1 self)
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Abstract. We show that the isomorphism of 3connected planar graphs can be decided in deterministic logspace. This improves the previously known bound UL ∩ coUL of [13]. 1
Oneinputface MPCVP is Hard for L, but in LogDCFL
"... A monotone planar circuit (MPC) is a Boolean circuit that can be embedded in a plane, and that has only AND and OR gates. Yang showed that the oneinputface monotone planar circuit value problem (MPCVP) is in NC 2, and Limaye et. al. improved the bound to LogCFL. Barrington et. al. showed that ev ..."
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Cited by 6 (3 self)
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A monotone planar circuit (MPC) is a Boolean circuit that can be embedded in a plane, and that has only AND and OR gates. Yang showed that the oneinputface monotone planar circuit value problem (MPCVP) is in NC 2, and Limaye et. al. improved the bound to LogCFL. Barrington et. al. showed that evaluating monotone upward stratified circuits, a restricted version of the oneinputface MPCVP, is in LogDCFL. In this paper, we prove that the unrestricted oneinputface MPCVP is also in LogDCFL. We also show this problem to be Lhard under quantifier free projections.
Space Efficient Algorithms for SeriesParallel Graphs
 IN 18TH INTERNATIONAL SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE (STACS), NUMBER 2010 IN LECTURE NOTES IN COMPUTER SCIENCE
, 2001
"... The subclass of directed seriesparallel graphs plays an important role in computer science. To determine whether a graph is seriesparallel is a well studied problem in algorithmic graph theory. Fast sequential and parallel algorithms for this problem have been developed in a sequence of papers ..."
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Cited by 5 (1 self)
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The subclass of directed seriesparallel graphs plays an important role in computer science. To determine whether a graph is seriesparallel is a well studied problem in algorithmic graph theory. Fast sequential and parallel algorithms for this problem have been developed in a sequence of papers. For seriesparallel graphs methods are also known to solve the reachability and the decomposition problem time efficiently. However, no dedicated results have been obtained for the space complexity of these problems  the topic of this paper. For this special class of graphs, we develop deterministic algorithms for the recognition, reachability, decomposition and the path counting problem that use only logarithmic space. Since for arbitrary directed graphs reachability and path counting are believed not to be solvable in logspace the main contribution of this work are novel deterministic path finding routines that work correctly in seriesparallel graphs, and a characterization...
The isomorphism problem for ktrees is complete for logspace, in
 Proceedings of 34th International Symposium Mathematical Foundations of Computer Science (MFCS), number 5734 in LNCS
, 2009
"... Abstract. We show that ktree isomorphism can be decided in logarithmic space by giving a logspace canonical labeling algorithm. This improves over the previous StUL upper bound and matches the lower bound. As a consequence, the isomorphism, the automorphism, as well as the canonization problem for ..."
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Cited by 5 (1 self)
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Abstract. We show that ktree isomorphism can be decided in logarithmic space by giving a logspace canonical labeling algorithm. This improves over the previous StUL upper bound and matches the lower bound. As a consequence, the isomorphism, the automorphism, as well as the canonization problem for ktrees are all complete for deterministic logspace. We also show that even simple structural properties of ktrees are complete for logspace.
Space efficient algorithms for directed seriesparallel graphs
, 2002
"... The subclass of directed seriesparallel graphs plays an important role in computer science. Whether a given graph is seriesparallel is a well studied problem in algorithmic graph theory, for which fast sequential and parallel algorithms have been developed in a sequence of papers. Also methods are ..."
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Cited by 4 (0 self)
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The subclass of directed seriesparallel graphs plays an important role in computer science. Whether a given graph is seriesparallel is a well studied problem in algorithmic graph theory, for which fast sequential and parallel algorithms have been developed in a sequence of papers. Also methods are known to solve the reachability and the decomposition problem for seriesparallel graphs time efficiently. However, no dedicated results have been obtained for the space complexity of these problems when restricted to seriesparallel graphs – the topic of this paper. Deterministic algorithms are presented for the recognition, reachability, decomposition and the path counting problem for seriesparallel graphs that use only logarithmic space. Since for arbitrary directed graphs reachability and path counting are believed not to be solvable in Logspace the main contribution of this work are novel deterministic path finding routines that work correctly in seriesparallel graphs, and a characterization of seriesparallel graphs by forbidden subgraphs that can be tested spaceefficiently. The space bounds are best possible, i.e. the decision problem is shown to be £complete with respect to AC^0reductions. They have also implications for the parallel time complexity of these problems when restricted to seriesparallel graphs. Finally, we sketch how these results can be generalised to extension of the seriesparallel graph family: to graphs with multiple sources or multiple sinks and to the class of minimal vertex seriesparallel graphs.