Given a pattern graph H with l edges, and a host graph G guaranteed to contain at most one occurrence of a subgraph isomorphic to H, we show that the time complexity of the problem of finding such an occurrence (if an...
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Given a pattern graph H with l edges, and a host graph G guaranteed to contain at most one occurrence of a subgraph isomorphic to H, we show that the time complexity of the problem of finding such an occurrence (if any) in G as well as that of the decision version of the problem are within a multiplicative factor O(l) of the time complexity for the corresponding problem in the general case, when G may contain several occurrences of H. It follows that for pattern graphs of constant size, the aforementioned uniqueness guarantee cannot yield any asymptotic speed up. We also derive analogous results with the analogous multiplicative factor linear in the number of vertices of H in the induced case when occurrences of induced subgraphs of G isomorphic to H are sought.
For a graph G = (V, E), a dominating set is a set D subset of V such that every vertex v is an element of V\D has a neighbor in D. Given a graph G = (V, E) and a positive integer k, the minimum outer-connected dominat...
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For a graph G = (V, E), a dominating set is a set D subset of V such that every vertex v is an element of V\D has a neighbor in D. Given a graph G = (V, E) and a positive integer k, the minimum outer-connected dominating set problem for G is to decide whether G has a dominating set D of cardinality at most k such that G[V\D] , the induced subgraph by G on V\D, is connected. In this paper, we consider the complexity of the minimum outer-connected dominating set problem for the class of chordal graphs. In particular, we show that the minimum outer-connected dominating set problem is NP-complete for doubly chordal graphs and undirected path graphs, two well studied subclasses of chordal graphs. We also give a linear time algorithm for computing a minimum outer-connected dominating set in proper interval graphs. Notice that proper interval graphs form a subclass of undirected path graphs as well as doubly chordal graphs. Crown Copyright (C) 2013 Published by Elsevier B.V. All rights reserved.
A total coloring of a graph G is a coloring of the vertices and edges of G such that no adjacent vertices, no adjacent edges, and no edge and its end-vertices are assigned the same color. We say a graph G is subcubic,...
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A total coloring of a graph G is a coloring of the vertices and edges of G such that no adjacent vertices, no adjacent edges, and no edge and its end-vertices are assigned the same color. We say a graph G is subcubic, if G has maximum degree at most three. In this paper we provide a concise proof for total 5-coloring subcubic graphs. (C) 2013 Elsevier B.V. All rights reserved.
Khuller and Schieber (1992) in [1] developed a constructive algorithm to prove that the existence of k-vertex independent trees in a k-vertex connected graph implies the existence of k-edge independent trees in a k-ed...
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Khuller and Schieber (1992) in [1] developed a constructive algorithm to prove that the existence of k-vertex independent trees in a k-vertex connected graph implies the existence of k-edge independent trees in a k-edge connected graph. In this paper, we show a counterexample where their algorithm fails. (C) 2013 Elsevier B.V. All rights reserved.
Testing a graph on 2-vertex- and 2-edge-connectivity are two fundamental algorithmic graph problems. For both problems, different linear-time algorithms with simple implementations are known. Here, an even simpler lin...
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Testing a graph on 2-vertex- and 2-edge-connectivity are two fundamental algorithmic graph problems. For both problems, different linear-time algorithms with simple implementations are known. Here, an even simpler linear-time algorithm is presented that computes a structure from which both the 2-vertex- and 2-edge-connectivity of a graph can be easily "read off". The algorithm computes all bridges and cut vertices of the input graph in the same time. (C) 2013 Elsevier B.V. All rights reserved.
Given a graph G and an odd cycle transversal T, we describe an elegant 0*(2(vertical bar T vertical bar)) algorithm for determining whether G has a smaller odd cycle transversal that is disjoint from T. We believe tha...
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Given a graph G and an odd cycle transversal T, we describe an elegant 0*(2(vertical bar T vertical bar)) algorithm for determining whether G has a smaller odd cycle transversal that is disjoint from T. We believe that our algorithm, based on a reduction to VERTEX COVER, is conceptually simpler than the known algorithms for the problem and refines the understanding of the relationship between ODD CYCLE TRANSVERSAL and VERTEX COVER. (C) 2013 Elsevier B.V. All rights reserved.
Extensional acyclic digraphs are acyclic digraphs whose vertices have pairwise different sets of out-neighbors;they represent hereditarily finite sets, which stand at the basis of some computer languages. In this pape...
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Extensional acyclic digraphs are acyclic digraphs whose vertices have pairwise different sets of out-neighbors;they represent hereditarily finite sets, which stand at the basis of some computer languages. In this paper we give an O (n(3)) algorithm for generating uniformly at random an extensional acyclic digraph on n vertices. This is done by first proposing a linear-time algorithm for encoding such digraphs by particular (n - 1)-tuples of subsets of {0, ..., n - 2}. We then give a new counting recurrence for such tuples, which we exploit in ranking/unranking algorithms. These are also useful for indexing data structures by hereditarily finite sets. (C) 2013 Elsevier B.V. All rights reserved.
The Maximum Weight Independent Set (mWIS) Problem on graphs with vertex weights asks for a set of pairwise nonadjacent vertices of maximum total weight. Being one of the most investigated problem on graphs, it is well...
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The Maximum Weight Independent Set (mWIS) Problem on graphs with vertex weights asks for a set of pairwise nonadjacent vertices of maximum total weight. Being one of the most investigated problem on graphs, it is well known to be NP-complete and hard to approximate. Several graph classes for which MWIS can be solved in polynomial time have been introduced in the literature. This note shows that MWIS can be solved in polynomial time for (P-6, co-banner)-free graphs - where a P-6 is an induced path of 6 vertices and a co-banner is a graph with vertices a, b, c, d, e and edges al), bc, cd, ce, de - so extending different analogous known results for other graph classes, namely, P-4-free, 2K(2)-free, (P-5, co-banner)-free, and (P-6, triangle)-free graphs. The solution algorithm is based on an idea/algorithm of Farber (1989) [10], leading to a dynamic programming approach for MWIS, and needs none of the aforementioned known results as sub-procedure. (C) 2012 Published by Elsevier B.V.
The GPU is an efficient accelerator for regular data-parallel workloads, but GPU acceleration is more difficult for graph algorithms and other applications with irregular memory access patterns and large memory footpr...
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The GPU is an efficient accelerator for regular data-parallel workloads, but GPU acceleration is more difficult for graph algorithms and other applications with irregular memory access patterns and large memory footprints. The minimum spanning tree (MST) problem arises in a variety of applications and its solution exemplifies the difficulties of mapping irregular algorithms to the GPU. In this paper, we present a memory-efficient parallel algorithm for finding the minimum spanning tree of very large graphs by introducing a data-parallel implementation of Kruskal's algorithm. We test scalability and performance on random and real-world graphs with up to 25 million vertices and 240 million edges on an Nvidia Tesla T10 GPU with 4GB of memory. Our method can process graphs 4X larger and up to 10X faster than was possible with the recently published implementation of Boruvka's MST algorithm for the GPU. We also demonstrate the performance advantage of the proposed method against the multi-core filter-Kruskal's MST algorithm on a dual quad-core CPU server with Nehalem X5550 processors.
This article presents a new deterministic algorithm for decremental maintenance of the transitive closure in a directed graph. The algorithm processes any sequence of edge deletions in O(mn) time and answers queries i...
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This article presents a new deterministic algorithm for decremental maintenance of the transitive closure in a directed graph. The algorithm processes any sequence of edge deletions in O(mn) time and answers queries in constant time. Previously, such time bound has only been achieved by a randomized Las Vegas algorithm. In addition to that, a few decremental algorithms for maintaining strongly connected components are shown, whose time complexity is O(n(1.5)) for planar graphs, O(n log n) for graphs with bounded treewidth and O(mn) for general digraphs.
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