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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 13 (5 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
www.stacsconf.org THE ISOMORPHISM PROBLEM FOR PLANAR 3CONNECTED GRAPHS IS IN UNAMBIGUOUS LOGSPACE
, 2008
"... Abstract. 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 AC 1. In this paper we improve the upper bound for planar 3connected graphs to unambiguo ..."
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Abstract. 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 AC 1. In this paper we improve the upper bound for planar 3connected graphs
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 13 (3 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
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 24 (6 self)
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We show that the stconnectivity problem for directed planar graphs can be decided in unambiguous logarithmic space. 1.
Longest Paths in Planar DAGs in Unambiguous Logspace
, 2009
"... Reachability and distance computation are known to be NLcomplete in general graphs, but within UL ∩ coUL if the graphs are planar. However, finding longest paths is known to be NPcomplete, even for planar graphs. We show that with the combination of planarity and acyclicity, finding the length of ..."
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Cited by 1 (0 self)
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Reachability and distance computation are known to be NLcomplete in general graphs, but within UL ∩ coUL if the graphs are planar. However, finding longest paths is known to be NPcomplete, even for planar graphs. We show that with the combination of planarity and acyclicity, finding the length
On the Power of Unambiguity in Logspace
, 2010
"... We report progress on the NL vs UL problem. We show unconditionally that the complexity class ReachFewL ⊆ UL. This improves on the earlier known upper bound ReachFewL ⊆ FewL. We investigate the complexity of minuniqueness a central notion in studying the NL vs UL problem. – We show that minuniq ..."
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Cited by 4 (2 self)
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L[log n] = UOptL[log n], (b) LogFew ≤ UOptL[log n] ≤ SPL. We show that the reachability problem over graphs embedded on 3 pages is complete for NL. This contrasts with the reachability problem over graphs embedded on 2 pages which is logspace equivalent to the reachability problem in planar graphs
A Framework for Dynamic Graph Drawing
 CONGRESSUS NUMERANTIUM
, 1992
"... Drawing graphs is an important problem that combines flavors of computational geometry and graph theory. Applications can be found in a variety of areas including circuit layout, network management, software engineering, and graphics. The main contributions of this paper can be summarized as follows ..."
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Cited by 627 (44 self)
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Drawing graphs is an important problem that combines flavors of computational geometry and graph theory. Applications can be found in a variety of areas including circuit layout, network management, software engineering, and graphics. The main contributions of this paper can be summarized
Monotone Complexity
, 1990
"... We give a general complexity classification scheme for monotone computation, including monotone spacebounded and Turing machine models not previously considered. We propose monotone complexity classes including mAC i , mNC i , mLOGCFL, mBWBP , mL, mNL, mP , mBPP and mNP . We define a simple ..."
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Cited by 2837 (11 self)
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simple notion of monotone reducibility and exhibit complete problems. This provides a framework for stating existing results and asking new questions. We show that mNL (monotone nondeterministic logspace) is not closed under complementation, in contrast to Immerman's and Szelepcs &apos
Primitives for the manipulation of general subdivisions and the computations of Voronoi diagrams
 ACM Tmns. Graph
, 1985
"... The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms ar ..."
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Cited by 543 (11 self)
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The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms
Results 1  10
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24,194