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58,501
Connecting obstacles in vertexdisjoint paths
 In 26th European Workshop Comp Geom
, 2010
"... Given a set of k disjoint convex polygonal obstacles inside a triangular container, we add straightline noncrossing edges such that each obstacle has three vertexdisjoint paths to the container. We prove combinatorial bounds on the minimum number of edges that are always sufficient and sometimes n ..."
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Cited by 2 (1 self)
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Given a set of k disjoint convex polygonal obstacles inside a triangular container, we add straightline noncrossing edges such that each obstacle has three vertexdisjoint paths to the container. We prove combinatorial bounds on the minimum number of edges that are always sufficient and sometimes
Degree Condition for VertexDisjoint Paths.
"... Let G be a connected graph of order n 1 + : : : + n k , where n i 2 are integers, for all 1 i k, and suppose the minimum degree of G is b n1 2 c + : : : + b n k 2 c. We prove that G contains k vertexdisjoint paths of orders n 1 ; : : : ; n k , unless it is an exceptional graph. The ex ..."
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Let G be a connected graph of order n 1 + : : : + n k , where n i 2 are integers, for all 1 i k, and suppose the minimum degree of G is b n1 2 c + : : : + b n k 2 c. We prove that G contains k vertexdisjoint paths of orders n 1 ; : : : ; n k , unless it is an exceptional graph
Vertex Disjoint Paths for Dispatching in Railways ∗
"... We study variants of the vertex disjoint paths problem in planar graphs where paths have to be selected from a given set of paths. We study the problem as a decision, maximization, and routinginrounds problem. Although all considered variants are NPhard in planar graphs, restrictions on the locati ..."
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Cited by 1 (0 self)
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We study variants of the vertex disjoint paths problem in planar graphs where paths have to be selected from a given set of paths. We study the problem as a decision, maximization, and routinginrounds problem. Although all considered variants are NPhard in planar graphs, restrictions
Construction of vertexdisjoint paths in alternating group networks
 J SUPERCOMPUT
, 2009
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Dominator Tree Verification and VertexDisjoint Paths
, 2005
"... We present a lineartime algorithm that given a flowgraph G = (V, A, r) and a tree T, checks whether T is the dominator tree of G. Also we prove that there exist two spanning trees of G, T1 and T2, such that for any vertex v the paths from r to v in T1 and T2 intersect only at the vertices that domi ..."
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Cited by 11 (8 self)
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We present a lineartime algorithm that given a flowgraph G = (V, A, r) and a tree T, checks whether T is the dominator tree of G. Also we prove that there exist two spanning trees of G, T1 and T2, such that for any vertex v the paths from r to v in T1 and T2 intersect only at the vertices
The planar directed kvertexdisjoint paths problem is fixedparameter tractable
 CORR
"... Given a graph G and k pairs of vertices (s1, t1),..., (sk, tk), the kVertexDisjoint Paths problem asks for pairwise vertexdisjoint paths P1,..., Pk such that Pi goes from si to ti. Schrijver [SICOMP’94] proved that the kVertexDisjoint Paths problem on planar directed graphs can be solved in ti ..."
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Cited by 3 (0 self)
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Given a graph G and k pairs of vertices (s1, t1),..., (sk, tk), the kVertexDisjoint Paths problem asks for pairwise vertexdisjoint paths P1,..., Pk such that Pi goes from si to ti. Schrijver [SICOMP’94] proved that the kVertexDisjoint Paths problem on planar directed graphs can be solved
Approximation algorithms for minimumtime broadcast under the vertexdisjoint paths mode
 In 9th Annual European Symposium on Algorithms (ESA '01), volume 2161 of LNCS
, 2001
"... We give a polynomialtime O( log n log OPT)approximation algorithm for minimumtime broadcast and minimumtime multicast in nnode networks under the singleport vertexdisjoint paths mode. This improves a previous approximation algorithm by Kortsarz and Peleg. In contrast, we give an (log n) lower ..."
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Cited by 8 (2 self)
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We give a polynomialtime O( log n log OPT)approximation algorithm for minimumtime broadcast and minimumtime multicast in nnode networks under the singleport vertexdisjoint paths mode. This improves a previous approximation algorithm by Kortsarz and Peleg. In contrast, we give an (log n
An Efficient Algorithm for the VertexDisjoint Paths Problem in Random Graphs
, 1996
"... Given a graph G = (V, E) and a set of pairs of vertices in V, we are interested in finding for each pair (ui, b;) a path connecting ai to bi, such that the set of paths so found is vertexdisjoint, (The problem is M/Pcomplete for general graphs as well as for planar graphs. It is in P if the number ..."
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Cited by 5 (0 self)
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Given a graph G = (V, E) and a set of pairs of vertices in V, we are interested in finding for each pair (ui, b;) a path connecting ai to bi, such that the set of paths so found is vertexdisjoint, (The problem is M/Pcomplete for general graphs as well as for planar graphs. It is in P
Dissemination of Information in VertexDisjoint Paths Mode, Part 2: Gossiping in dDimensional Grids and Planar Graphs
 COMPUTER AND ARTI INTELLIGENCE
, 1993
"... This paper continues with the study of the communication modes introduced in [J. Hromkovic, R. Klasing, E.A. St¨ohr, "Dissemination of Information in VertexDisjoint Paths Mode, Part 1: General Bounds and Gossiping in HypercubeLike Networks", submitted to Information and Computation. (Ext ..."
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Cited by 8 (1 self)
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This paper continues with the study of the communication modes introduced in [J. Hromkovic, R. Klasing, E.A. St¨ohr, "Dissemination of Information in VertexDisjoint Paths Mode, Part 1: General Bounds and Gossiping in HypercubeLike Networks", submitted to Information and Computation
Results 1  10
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58,501