Let G be a directed graph. A 2-directed block in G is a maximal vertex set C-2d subset of V with vertical bar C-2d vertical bar >= 2 such that for each pair of distinct vertices x, y is an element of C-2d, there ex...
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Let G be a directed graph. A 2-directed block in G is a maximal vertex set C-2d subset of V with vertical bar C-2d vertical bar >= 2 such that for each pair of distinct vertices x, y is an element of C-2d, there exist two vertex-disjoint paths from x to y and two vertex-disjoint paths from y to x in G. In this paper we present two algorithms for computing the 2-directed blocks of G in O(min{m, (t(sap) + t(sb))n}n) time, where tsap is the number of the strong articulation points of G and tsb is the number of the strong bridges of G. Furthermore, we study two related concepts: the 2-strong blocks and the 2-edge blocks of G. We give two algorithms for computing the 2-strong blocks of G in O(min{m, t(sap)n}n) time and we show that the 2-edge blocks of G can be computed in O(min{m, t(sb)n}n) time. In this paper we also study some optimization problems related to the strong articulation points and the 2-blocks of a directed graph. Given a strongly connected graph G = (V, E), we want to find a minimum strongly connected spanning subgraph G* = (V, E*) of G such that the strong articulation points of G coincide with the strong articulation points of G*. We show that there is a linear time 17/3 approximation algorithm for this NP-hard problem. We also consider the problem of finding a minimum strongly connected spanning subgraph with the same 2-blocks in a strongly connected graph G. We present approximation algorithms for three versions of this problem, depending on the type of 2-blocks.
We investigate graphs whose matching polynomial has six distinct roots. We show that for those graphs if its order n > 6 then they are determined by their matching polynomials. (C) 2014 Elsevier B.V. All rights res...
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We investigate graphs whose matching polynomial has six distinct roots. We show that for those graphs if its order n > 6 then they are determined by their matching polynomials. (C) 2014 Elsevier B.V. All rights reserved.
In this article, we will study the topological sorts of two directed acyclic graphs (DAGs) and the associated properties. More specifically, we will study under what conditions a certain single (or some, or every) top...
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In this article, we will study the topological sorts of two directed acyclic graphs (DAGs) and the associated properties. More specifically, we will study under what conditions a certain single (or some, or every) topological sort(s) of a DAG can be extended into the topological sort(s) of another DAG. We first give the necessary and sufficient conditions for the problems. We then indicate that these problems are solvable either in linear time cost or in the same time cost as to compute the transitive closure. (C) 2014 Elsevier B.V. All rights reserved.
In this note we show a one-to-one correspondence between potentially optimal solutions to the cluster deletion problem in a graph G and potentially optimal solutions for the minimum sum coloring problem in (G) over ba...
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In this note we show a one-to-one correspondence between potentially optimal solutions to the cluster deletion problem in a graph G and potentially optimal solutions for the minimum sum coloring problem in (G) over bar (i.e. the complement graph of G). We apply this correspondence to polynomially solve the cluster deletion problem in a subclass of P-4-sparse graphs that strictly includes P-4-reducible graphs. (c) 2015 Elsevier B.V. All rights reserved.
A wireless network with a mesh topology works reliably and offers redundancy. In modern broadband wireless mesh networks using OFDMA techniques, the problems of time, frequency, are more complicated from a cellular sy...
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ISBN:
(纸本)9783800742530
A wireless network with a mesh topology works reliably and offers redundancy. In modern broadband wireless mesh networks using OFDMA techniques, the problems of time, frequency, are more complicated from a cellular system, due to system architecture and distributed control and management. This paper focuses on OFDMA wireless mesh network systems and the problem of time/frequency resource allocation, particularly with regard to subcarriers. Advanced graph theory tools are used for time/frequency resource allocation in an arbitrary architecture using to and for a square grid allocation and allow frequency reuse.
Given two sets A and B of integers, we consider the problem of finding a set S subset of A of the smallest possible cardinality such the greatest common divisor of the elements of S boolean OR B equals that of those o...
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Given two sets A and B of integers, we consider the problem of finding a set S subset of A of the smallest possible cardinality such the greatest common divisor of the elements of S boolean OR B equals that of those of A boolean OR B. The particular cases of B = empty set and #B = 1 are of special interest and have some links with graph theory. We also consider the corresponding question for the least common multiple of the elements. We establish NP-completeness and approximation results for these problems by relating them to the Set Cover Problem. (C) 2014 Elsevier B.V. All rights reserved.
A p-star is a complete bipartite graph K-1,K-p with one center node and p leaves. In this paper, we propose a polynomial self-stabilizing algorithm for maximal graph decomposition into p-stars. Given an arbitrary grap...
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A p-star is a complete bipartite graph K-1,K-p with one center node and p leaves. In this paper, we propose a polynomial self-stabilizing algorithm for maximal graph decomposition into p-stars. Given an arbitrary graph G and a positive integer p >= 1, this decomposition provides disjoint components of G, such that each component induces a p-star in G. Under the unfair distributed scheduler, the algorithm converges within O (Delta(2)m) moves where m is the number of edges and Delta is maximum node degree in the graph G. (C) 2015 Elsevier B.V. All rights reserved.
Given an undirected graph, each of the two end-vertices of an edge can "own" the edge. Call a vertex "poor" if it owns at most one edge. We give a polynomial time algorithm for the problem of findi...
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Given an undirected graph, each of the two end-vertices of an edge can "own" the edge. Call a vertex "poor" if it owns at most one edge. We give a polynomial time algorithm for the problem of finding an assignment of owners to the edges which minimizes the number of poor vertices. In the terminology of graph orientation, this means finding an orientation for the edges of a graph which minimizes the number of vertices with out-degree at most 1, and answers a question of Asahiro et al. (2013). (C) 2015 Elsevier B.V. All rights reserved.
A temporal network is a directed graph in which each arc has a time label specifying the time at which its end vertices communicate. An arborescence in a temporal network is said to be time-respecting, if the time lab...
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A temporal network is a directed graph in which each arc has a time label specifying the time at which its end vertices communicate. An arborescence in a temporal network is said to be time-respecting, if the time labels on every directed path from the root in this arborescence are monotonically non-decreasing. In this paper, we consider a characterization of the existence of arc-disjoint time-respecting arborescences in temporal networks. (C) 2014 Elsevier B.V. All rights reserved.
We develop a linear-space O(n + m) time algorithm to solve the cluster editing problem for proper interval models, where n and m are the number of vertices and edges of the represented graph. (C) 2015 Elsevier B.V. Al...
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We develop a linear-space O(n + m) time algorithm to solve the cluster editing problem for proper interval models, where n and m are the number of vertices and edges of the represented graph. (C) 2015 Elsevier B.V. All rights reserved.
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