Results 1  10
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16
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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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
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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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 minuniqueness is necessary and sufficient for showing NL = UL. – We revisit the class OptL[log n] and show that ShortestPathLength computing the length of the shortest path in a DAG, is complete for OptL[log n]. – We introduce UOptL[log n], an unambiguous version of OptL[log n], and show that (a) NL = UL if and only if OptL[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 and hence is in UL.
Reachability Problems: An Update
"... Abstract. There has been a great deal of progress in the fifteen years that have elapsed since Wigderson published his survey on the complexity of the graph connectivity problem [Wig92]. Most significantly, Reingold solved the longstanding question of the complexity of the st connectivity problem i ..."
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Abstract. There has been a great deal of progress in the fifteen years that have elapsed since Wigderson published his survey on the complexity of the graph connectivity problem [Wig92]. Most significantly, Reingold solved the longstanding question of the complexity of the st connectivity problem in undirected graphs, showing that this is complete for logspace (L) [Rei05]. This survey talk will focus on some of the remaining open questions dealing with graph reachability problems. Particular attention will be paid to these topics: – Reachability in planar directed graphs (and more generally, in graphs of low genus) [ADR05,BTV07]. – Reachability in different classes of grid graphs [ABC + 06]. – Reachability in mangroves [AL98]. The problem of finding a path from one vertex to another in a graph is the first problem that was identified as being complete for a natural subclass of P; it was shown to be complete for nondeterministic logspace (NL) by Jones [Jon75]. Restricted versions of this problem were subsequently shown to be complete for other natural complexity
Kissinger: Web Service Composition using Service Suggestions
 In: Proceedings of the 2011 IEEE International Workshop on Formal Methods in Services and Cloud Computing
, 2011
"... Abstract — This paper presents a semiautomatic Web service composition approach. This approach ranks all available candidate Web service operations based on semantic annotations and suggests service operations to a human designer during the process of Web service composition. The ranking scores are ..."
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Abstract — This paper presents a semiautomatic Web service composition approach. This approach ranks all available candidate Web service operations based on semantic annotations and suggests service operations to a human designer during the process of Web service composition. The ranking scores are based on data mediation, functionality and formal service specifications. A formal graph model, an IODAG, is defined to formalize an input/output schema of a Web service operation. Three data mediation algorithms are developed to handle the data heterogeneities arising during Web service composition. The data mediation algorithms analyze the schemas of the inputs and outputs of service operations and consider the structures of the schemas. A typed representation for our data mediation approach, which formalizes the data mediation problem as a subtypechecking problem, is presented. An evaluation is performed to study the effectiveness of different data mediation and service suggestion algorithms used to assist designers composing Web services. KeywordsWeb service composition, data mediation, service suggestions, semantic annotations, SAWSDL I.
The Complexity of Planar Graph Isomorphism
"... The Graph Isomorphism problem restricted to planar graphs has been known to be solvable in polynomial time many years ago. In terms of complexity classes however, the exact complexity of the problem has been established only very recently. It was proved in [6] that planar graph isomorphism can be co ..."
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The Graph Isomorphism problem restricted to planar graphs has been known to be solvable in polynomial time many years ago. In terms of complexity classes however, the exact complexity of the problem has been established only very recently. It was proved in [6] that planar graph isomorphism can be computed within logarithmic space. Since there is a matching hardness result [12], this shows that the problem is complete for L. Although this could be considered as a result in algorithmics its proof relies on several important new developments in the area of logarithmic space complexity classes and reflects the close connections between algorithms and complexity theory. In this column we give an overview of this result mentioning the developments that led to it. 1
A logspace algorithm for canonization of planar graphs
, 2008
"... Planar graph canonization is known to be hard for L this directly follows from Lhardness of treecanonization [Lin92]. We give a logspace algorithm for planar graph canonization. This gives completeness for logspace under AC 0 manyone reductions and improves the previously known upper bound of A ..."
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Planar graph canonization is known to be hard for L this directly follows from Lhardness of treecanonization [Lin92]. We give a logspace algorithm for planar graph canonization. This gives completeness for logspace under AC 0 manyone reductions and improves the previously known upper bound of AC 1 [MR91]. A planar graph can be decomposed into biconnected components. We give a logspace procedure for the decomposition of a biconnected planar graph into a triconnected component tree. The canonization process is based on these decomposition steps. 1
Longest Paths in Planar DAGs in Unambiguous Logspace
"... 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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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 the longest path (and also enumerating one such path) is also in UL ∩ coUL. The result extends to toroidal DAGs as well. We also address the question of when reachability, distance, and longest path are indeed equivalent on DAGs, and give partial bounds. When the number of distinct paths is bounded by a polynomial, counting the number of paths is known to be in NL. We show that for planar DAGs with this promise, counting can be done by a UAuxPDA in polynomial time. The UAuxPDA(poly) bound also holds if we want to compute the number of longest paths, or shortest paths, and this number is bounded by a polynomial (irrespective of the total number of paths). Along the way, we show that counting in general DAGs is possible in LogDCFL provided the number of paths is bounded by a polynomial and the target node is the only sink.
Deterministic Simulations and Hierarchy . . .
, 2010
"... In this dissertation, we present three research directions related to the question whether all randomized algorithms can be derandomized, i.e., simulated by deterministic algorithms with a small loss in efficiency. TypicallyCorrect Derandomization A recent line of research has considered “typically ..."
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In this dissertation, we present three research directions related to the question whether all randomized algorithms can be derandomized, i.e., simulated by deterministic algorithms with a small loss in efficiency. TypicallyCorrect Derandomization A recent line of research has considered “typicallycorrect” deterministic simulations of randomized algorithms, which are allowed to err on few inputs. Such derandomizations may be easier to obtain and/or be more efficient than full derandomizations that do not make mistakes. We further the study of typicallycorrect derandomization in two ways. First, we develop a generic approach for constructing typicallycorrect derandomizations based on seedextending pseudorandom generators, which are pseudorandom generators that reveal their seed. We use our approach to obtain both conditional and unconditional typicallycorrect derandomization results in various algorithmic settings. For example, we present a typicallycorrect polynomialtime simulation for every language in BPP based on
ReachFewL = ReachUL
, 2011
"... We show that two complexity classes introduced about two decades ago are equal. ReachUL is the class of problems decided by nondeterministic logspace machines which on every input have at most one computation path from the start configuration to any other configuration. ReachFewL, a natural general ..."
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We show that two complexity classes introduced about two decades ago are equal. ReachUL is the class of problems decided by nondeterministic logspace machines which on every input have at most one computation path from the start configuration to any other configuration. ReachFewL, a natural generalization of ReachUL, is the class of problems decided by nondeterministic logspace machines which on every input have at most polynomially many computation paths from the start configuration to any other configuration. We show that ReachFewL = ReachUL. 1