A subset L subset of V of a graph G = (V, E) is called a connected liar's dominating set of G if (i) for all v. V, |NG[v] n L| >= 2, ( ii) for every pair u, v is an element of V of distinct vertices, |(N-G[u]. ...
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A subset L subset of V of a graph G = (V, E) is called a connected liar's dominating set of G if (i) for all v. V, |NG[v] n L| >= 2, ( ii) for every pair u, v is an element of V of distinct vertices, |(N-G[u]. N-G[v]) boolean AND L| >= 3, and ( iii) the induced subgraph of G on L is connected. In this paper, we initiate the algorithmic study of minimum connected liar's domination problem by showing that the corresponding decision version of the problem is NP-complete for general graph. Next we study this problem in subclasses of chordal graphs where we strengthen the NP-completeness of this problem for undirected path graph and prove that this problem is linearly solvable for block graphs. Finally, we propose an approximation algorithm for minimum connected liar's domination problem and investigate its hardness of approximation in general graphs.
In this paper, we study the minimum energy multicast problem with reception cost in wireless sensor networks. Suppose there are n nodes in the network. Each node v has l(v) transmission power levels to be chosen and i...
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ISBN:
(纸本)9783642226151
In this paper, we study the minimum energy multicast problem with reception cost in wireless sensor networks. Suppose there are n nodes in the network. Each node v has l(v) transmission power levels to be chosen and its reception cost is B(v) if it receives a message. The problem of our concerning is: given a multicast request, how to find a multicast tree such that the total energy cost of the multicast tree including transmitting cost and reception cost is minimized. We firstly propose a general algorithm Fix-MEM-R-G for the case while each node has the fixed power level. Based on Fix-MEM-R-G algorithm, we propose an approximation algorithm. We also propose a heuristic algorithm for this special case. For the general case that each node has multiple power levels, we propose a. general algorithm NF-MEM-R-G and an approximation algorithm based on NF-MEM-R-G, algorithm. We also propose a. heuristic algorithm for general case.
The polynomial-time solvable k-hurdle problem is a natural generalization of the classical s-t minimum cut problem where we must select a minimum-cost subset S of the edges of a graph such that vertical bar p boolean ...
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The polynomial-time solvable k-hurdle problem is a natural generalization of the classical s-t minimum cut problem where we must select a minimum-cost subset S of the edges of a graph such that vertical bar p boolean AND S vertical bar >= k for every s-t path p. In this paper, we describe a set of approximation algorithms for "k-hurdle" variants of the NP-hard multiway cut and multicut problems. For the k-hurdle multiway cut problem with r terminals, we give two results, the first being a pseudo-approximation algorithm that outputs a (k - 1)-hurdle solution whose cost is at most that of an optimal solution for k hurdles. Secondly, we provide a 2(1 - 1/r)-approximation algorithm based on rounding the solution of a linear program, for which we give a simple randomized half-integrality proof that works for both edge and vertex k-hurdle multiway cuts that generalizes the half-integrality results of Garg et al. for the vertex multiway cut problem. We also describe an approximation-preserving reduction from vertex cover as evidence that it may be difficult to achieve a better approximation ratio than 2(1 - 1/r). For the k-hurdle multicut problem in an n-vertex graph, we provide an algorithm that, for any constant epsilon > 0, outputs a inverted right perpendicular(1 - epsilon)kinverted left perpendicular-hurdle solution of cost at most O(log n) times that of an optimal k-hurdle solution, and we obtain a 2-approximation algorithm for trees.
We give a very simple approximation algorithm for the maximum asymmetric traveling salesman problem. The approximation guarantee of our algorithm is 2/3, which matches the best known approximation guarantee by Kaplan,...
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ISBN:
(纸本)9783939897354
We give a very simple approximation algorithm for the maximum asymmetric traveling salesman problem. The approximation guarantee of our algorithm is 2/3, which matches the best known approximation guarantee by Kaplan, Lewenstein, Shafrir and Sviridenko. Our algorithm is simple to analyze, and contrary to previous approaches, which need an optimal solution to a linear program, our algorithm is combinatorial and only uses maximum weight perfect matching algorithm.
The constrained minimum vertex cover problem on bipartite graphs (the Min-CVCB problem) is an important NP-complete problem. This paper presents a polynomial time approximation algorithm for the problem based on the t...
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The constrained minimum vertex cover problem on bipartite graphs (the Min-CVCB problem) is an important NP-complete problem. This paper presents a polynomial time approximation algorithm for the problem based on the technique of chain implication. For any given constant ??>?0, if an instance of the Min-CVCB problem has a minimum vertex cover of size (k_ u , k _l ), our algorithm constructs a vertex cover of size (k~* _u , k~* _l ), satisfying max {k~ *_u /k _u , k ~*_ l /k_ l }?≤?1?+??. Electronic supplementary material The online version of this article (doi: 10.1007/s11390-008-9180-5) contains supplementary material, which is available to authorized users.
A wireless ad-hoc network consists of a number of wireless devices (nodes), that communicate with each other within the network using their built-in radio transceivers. The nodes are in general battery-powered, thus t...
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ISBN:
(纸本)9783642316388
A wireless ad-hoc network consists of a number of wireless devices (nodes), that communicate with each other within the network using their built-in radio transceivers. The nodes are in general battery-powered, thus their lifetime is limited. Therefore, algorithms for maximizing the network lifetime are of great interest. In this paper we consider the Rooted Maximum Network Lifetime (RMNL) problems: given a network N and a node r, the objective is to find a maximum-size collection of routing trees rooted at the node r for a specified communication pattern. The number of such trees represents the total number of communication rounds executed before the first node in the network dies due to battery depletion. We consider two communication patterns, broadcast and convergecast. We follow the approach used by Nutov and Segal in [15], who developed polynomial time approximation algorithms with constant approximation ratios for the broadcast and convergecast RMNL problems. Our analysis of their algorithms leads to better approximation ratios than the ratios derived in [15]. In particular, we show a 1/7 approximation ratio for the multiple topology convergecast RMNL problem, improving the previous ratio of 1/31.
The Capacitated Multicast Tree Routing Problem is considered, in which only a limited number of destination nodes are allowed to receive data in one routing tree and multiple routing trees are needed to send data from...
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ISBN:
(纸本)9783540850960
The Capacitated Multicast Tree Routing Problem is considered, in which only a limited number of destination nodes are allowed to receive data in one routing tree and multiple routing trees are needed to send data from the source node to all destination nodes. The goal is to minimize the total cost of these routing trees. An improved approximation algorithm is presented, which has a worst case performance ratio of 8/5 + 5/4 rho. Here rho denotes the best approximation ratio for the Steiner Minimum Tree problem, and it is about 1.55 at the writing of the paper. This improves upon the previous best having a performance ratio of 2+rho.
In this work we give a family of radical functions, C, uniformly dense in C [a, b]. This family does not satisfy the usual theorems of approximation Theory about C [a, b]. The mathematical expression of the sequence t...
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The max-coloring problem is to compute a legal coloring of the vertices of a graph G=(V,E) with vertex weights w such that is minimized, where C (1),aEuro broken vertical bar,C (k) are the various color classes. For g...
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The max-coloring problem is to compute a legal coloring of the vertices of a graph G=(V,E) with vertex weights w such that is minimized, where C (1),aEuro broken vertical bar,C (k) are the various color classes. For general graphs, max-coloring is as hard as the classical vertex coloring problem, a special case of the former where vertices have unit weight. In fact, in some cases it can even be harder: for example, no polynomial time algorithm is known for max-coloring trees. In this paper we consider the problem of max-coloring paths and its generalization, max-coloring skinny trees, a broad class of trees that includes paths and spiders. For these graphs, we show that max-coloring can be solved in time O(|V|+time for sorting the vertex weights). When vertex weights are real numbers, we show a matching lower bound of Omega(|V|log |V|) in the algebraic computation tree model.
A method of measurement of the coordinates of an object equipped with an acoustic radiator is proposed. The measurements are performed by means of a passive hydroacoustic detection and ranging system based on a networ...
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A method of measurement of the coordinates of an object equipped with an acoustic radiator is proposed. The measurements are performed by means of a passive hydroacoustic detection and ranging system based on a network of hydrophones. Digital processing of Doppler signals from the outputs of the hydrophones and a two-stage approximation algorithm are used. An example illustrating the implementation of the method is given and the errors of the method are considered.
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