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Kernels in planar digraphs
 In Optimization Online. Mathematical Programming Society
, 2001
"... A set S of vertices in a digraph D = (V, A) is a kernel if S is independent and every vertex in V − S has an outneighbor in S. We show that there exist O(n2 19.1 √ k + n 4)time and O(2 19.1 √ k k 9 + n 2)time algorithms for checking whether a planar digraph D of order n has a kernel with at most k ..."
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Cited by 17 (1 self)
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A set S of vertices in a digraph D = (V, A) is a kernel if S is independent and every vertex in V − S has an outneighbor in S. We show that there exist O(n2 19.1 √ k + n 4)time and O(2 19.1 √ k k 9 + n 2)time algorithms for checking whether a planar digraph D of order n has a kernel with at most
Acyclic Subgraphs of Planar Digraphs
, 2014
"... An acyclic set in a digraph is a set of vertices that induces an acyclic subgraph. In 2011, Harutyunyan conjectured that every planar digraph on n vertices without directed 2cycles possesses an acyclic set of size at least 3n/5. We prove this conjecture for digraphs where every directed cycle has l ..."
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An acyclic set in a digraph is a set of vertices that induces an acyclic subgraph. In 2011, Harutyunyan conjectured that every planar digraph on n vertices without directed 2cycles possesses an acyclic set of size at least 3n/5. We prove this conjecture for digraphs where every directed cycle has
Planar digraphs of digirth five are 2colorable
, 2014
"... NeumannLara (1985) and Škrekovski conjectured that every planar digraph with digirth at least three is 2colorable. We prove a relaxed version of this conjecture: every planar digraph of digirth at least five is 2colorable. The result also holds in the setting of list colorings. ..."
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NeumannLara (1985) and Škrekovski conjectured that every planar digraph with digirth at least three is 2colorable. We prove a relaxed version of this conjecture: every planar digraph of digirth at least five is 2colorable. The result also holds in the setting of list colorings.
Building blocks of upward planar digraphs
 Proc. GD’04, volume 3383 of LNCS
, 2005
"... The upward planarity testing problem consists of testing if a digraph admits a drawing Γ such that all edges in Γ are monotonically increasing in the vertical direction and no edges in Γ cross. In this paper we reduce the problem of testing a digraph for upward planarity to the problem of testing if ..."
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Cited by 1 (0 self)
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The upward planarity testing problem consists of testing if a digraph admits a drawing Γ such that all edges in Γ are monotonically increasing in the vertical direction and no edges in Γ cross. In this paper we reduce the problem of testing a digraph for upward planarity to the problem of testing
Efficient Algorithms for Shortest Path Queries in Planar Digraphs
 In Proceedings of the 22nd International Workshop on GraphTheoretic Concepts in Computer Science
, 1996
"... . This paper describes algorithms for answering shortest path queries in digraphs with small separators and, in particular, in planar digraphs. In this version of the problem, one has to preprocess the input graph so that, given an arbitrary pair of query vertices v and w, the shortestpath distance ..."
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Cited by 14 (0 self)
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. This paper describes algorithms for answering shortest path queries in digraphs with small separators and, in particular, in planar digraphs. In this version of the problem, one has to preprocess the input graph so that, given an arbitrary pair of query vertices v and w, the shortest
EFFICIENT PARALLEL ALGORITHMS FOR SHORTEST PATHS IN PLANAR DIGRAPHS
 BIT 32 (1992),215236
, 1992
"... Efficient parallel algorithms are presented, on the CREW PRAM model, for generating a succinct encoding of all pairs shortest path information in a directed planar graph G with realvalued edge costs but no negative cycles. We assume that a planar embedding of G is given, togetber with a set of q fa ..."
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Cited by 7 (4 self)
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Efficient parallel algorithms are presented, on the CREW PRAM model, for generating a succinct encoding of all pairs shortest path information in a directed planar graph G with realvalued edge costs but no negative cycles. We assume that a planar embedding of G is given, togetber with a set of q
Fast algorithms for maintaining shortest paths in outerplanar and planar digraphs
 Proceedings, lOth International Symposium on Fundamentals of Computation Theory, LNCS 965
, 1995
"... Abstract. We present algorithms for maintaining shortest path information in dynamic outerplanar digraphs with sublogarithmic query time. By choosing appropriate parameters we achieve continuous tradeoffs between the preprocessing, query, and update times. Our data structure is based on a recursi ..."
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Cited by 2 (0 self)
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recursive separator decomposition of the graph and it encodes the shortest paths between the members of a properly chosen subset of vertices. We apply this result to construct improved shortest path algorithms for dynamic planar digraphs. 1
Towards overcoming the transitiveclosure bottleneck: efficient parallel algorithms for planar digraphs
 J. Comput. System Sci
, 1993
"... Abstract. Currently, there is a significant gap between the best sequential and parallel complexities of many fundamental problems related to digraph reachability. This complexity bottleneck essentially reflects a seemingly unavoidable reliance on transitive closure techniques in parallel algorithms ..."
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Cited by 11 (1 self)
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algorithms for digraph reachability. To pinpoint the nature of the bottleneck, we de* velop a collection of polylogtime reductions among reachability problems. These reductions use only linear processors and work for general graphs. Furthermore, for planar digraphs, we give polylogtime algorithms
External Data Structures for Shortest Path Queries on Planar Digraphs
"... Abstract. In this paper we present spacequery tradeoffs for external memory data structures that answer shortest path queries on planar directed graphs. For any S = Ω(N 1+ɛ)andS = O(N 2 /B), our main result is a family of structures that use S space and answer queries in O ( N2 SB) I/Os, thus obta ..."
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Cited by 1 (0 self)
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Abstract. In this paper we present spacequery tradeoffs for external memory data structures that answer shortest path queries on planar directed graphs. For any S = Ω(N 1+ɛ)andS = O(N 2 /B), our main result is a family of structures that use S space and answer queries in O ( N2 SB) I/Os, thus
Results 1  10
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2,904