Results 1  10
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32
A new algorithm for finding trees with many leaves
, 2001
"... We present an algorithm that finds trees with at least k leaves in undirected and directed graphs. These problems are known as Maximum Leaf Spanning Tree for undirected graphs, and, respectively, Directed Maximum Leaf OutTree and Directed Maximum Leaf Spanning OutTree in the case of directed grap ..."
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Cited by 13 (2 self)
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We present an algorithm that finds trees with at least k leaves in undirected and directed graphs. These problems are known as Maximum Leaf Spanning Tree for undirected graphs, and, respectively, Directed Maximum Leaf OutTree and Directed Maximum Leaf Spanning OutTree in the case of directed graphs. The run time of our algorithm is O(poly(V ) + 4 k k 2) on undirected graphs, and O(4 k V ·E) on directed graphs. Currently, the fastest algorithms for these problems have run times of O(poly(n) + 6.75 k poly(k)) and 2 O(k log k) poly(n), respectively.
Constructing Minimum Connected Dominating Sets with Bounded Diameters in Wireless Networks
, 2009
"... Connected Dominating Sets (CDSs) can serve as virtual backbones for wireless networks. A smaller virtual backbone incurs less maintenance overhead. Unfortunately, computing a minimum size CDS is NPhard, and thus most researchers in this area concentrate on how to construct smaller CDSs. However, pe ..."
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Cited by 13 (8 self)
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Connected Dominating Sets (CDSs) can serve as virtual backbones for wireless networks. A smaller virtual backbone incurs less maintenance overhead. Unfortunately, computing a minimum size CDS is NPhard, and thus most researchers in this area concentrate on how to construct smaller CDSs. However, people neglected other important metrics of network, such as diameter and average hop distances between two communication parties. In this paper, we investigate the problem of constructing quality CDS in terms of size, diameter, and Average Backbone Path Length (ABPL). We present two centralized algorithms having constant performance ratios for its size and diameter of the constructed CDS. Especially, the size of CDS computed by the second algorithm is no more than 6.906 times of its optimal solution. Furthermore, we give its distributed version, which not only can be implemented in real situation easily but also considers energy to extend network lifetime. In our simulation, we show that in average the distributed algorithm not only generates a CDS with smaller diameter and ABPL than related work but also suppresses its size well. We also show that it is more energy efficient than others in prolonging network lifetime.
A New Constant Factor Approximation for Computing 3Connected mDominating Sets in Homogeneous Wireless Networks
"... Abstract—In this paper, we study the problem of constructing quality faulttolerant Connected Dominating Sets (CDSs) in homogeneous wireless networks, which can be defined as minimum kConnected mDominating Set ((k, m)CDS) problem in Unit Disk Graphs (UDGs). We found that every existing approximat ..."
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Cited by 11 (1 self)
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Abstract—In this paper, we study the problem of constructing quality faulttolerant Connected Dominating Sets (CDSs) in homogeneous wireless networks, which can be defined as minimum kConnected mDominating Set ((k, m)CDS) problem in Unit Disk Graphs (UDGs). We found that every existing approximation algorithm for this problem is incomplete for k ≥ 3 in a sense that it does not generate a feasible solution in some UDGs. Based on these observations, we propose a new polynomial time approximation algorithm for computing (3,m)CDSs. We also show that our algorithm is correct and its approximation ratio is a constant. I.
DisC Diversity: Result Diversification based on Dissimilarity and Coverage
, 2012
"... Recently, result diversification has attracted a lot of attention as a means to improve the quality of results retrieved by user queries. In this paper, we propose a new, intuitive definition of diversity called DisC diversity. A DisC diverse subset of a query result contains objects such that each ..."
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Cited by 10 (2 self)
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Recently, result diversification has attracted a lot of attention as a means to improve the quality of results retrieved by user queries. In this paper, we propose a new, intuitive definition of diversity called DisC diversity. A DisC diverse subset of a query result contains objects such that each object in the result is represented by a similar object in the diverse subset and the objects in the diverse subset are dissimilar to each other. We show that locating a minimum DisC diverse subset is an NPhard problem and provide heuristics for its approximation. We also propose adapting DisC diverse subsets to a different degree of diversification. We call this operation zooming. We present efficient implementations of our algorithms based on the Mtree, a spatial index structure, and experimentally evaluate their performance.
An exact algorithm for the maximum leaf spanning tree problem
 PROC. FOURTH INTERNATIONAL WORKSHOP ON PARAMETERIZED AND EXACT COMPUTATION. LECTURE NOTES IN COMPUTER SCIENCE
, 2009
"... Given an undirected graph with n nodes, the Maximum Leaf Spanning Tree problem is to find a spanning tree with as many leaves as possible. When parameterized in the number of leaves k, this problem can be solved in time O(4 k poly(n)) using a simple branching algorithm introduced by a subset of th ..."
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Cited by 6 (4 self)
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Given an undirected graph with n nodes, the Maximum Leaf Spanning Tree problem is to find a spanning tree with as many leaves as possible. When parameterized in the number of leaves k, this problem can be solved in time O(4 k poly(n)) using a simple branching algorithm introduced by a subset of the authors [12]. Daligault, Gutin, Kim, and Yeo [6] improved the branching and obtained a running time of O(3.72 k poly(n)). In this paper, we study the problem from an exponential time viewpoint, where it is equivalent to the Connected Dominating Set problem. Here, Fomin, Grandoni, and Kratsch showed how to break the Ω(2 n) barrier and proposed an O(1.9407 n)time algorithm [10]. In light of some useful properties of [12] and [6], we present a branching algorithm whose running time of O(1.8966 n) has been analyzed using the MeasureandConquer technique. Finally we provide a lower bound of Ω(1.4422 n) for the worst case running time of our algorithm.
An FPT Algorithm for Directed Spanning kLeaf
 PREPRINT 0462007, COMBINATORIAL OPTIMIZATION & GRAPH ALGORITHMS GROUP
, 2007
"... An outbranching of a directed graph is a rooted spanning tree with all arcs directed outwards from the root. We consider the problem of deciding whether a given digraph D has an outbranching with at least k leaves (Directed Spanning kLeaf). We prove that this problem is fixed parameter tractable, ..."
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Cited by 5 (0 self)
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An outbranching of a directed graph is a rooted spanning tree with all arcs directed outwards from the root. We consider the problem of deciding whether a given digraph D has an outbranching with at least k leaves (Directed Spanning kLeaf). We prove that this problem is fixed parameter tractable, when k is chosen as the parameter. Previously this was only known for restricted classes of directed graphs. The main new ingredient in our approach is a lemma that shows that given a locally optimal outbranching of a directed graph in which every arc is part of at least one outbranching, either an outbranching with at least k leaves exists, or a path decomposition with width O(k 3) can be found. This enables a dynamic programming based algorithm of running time 2 O(k3 log k) · n O(1), where n = V (D).
O(log n)Localized Algorithms on the Coverage Problem in Heterogeneous Sensor Networks
"... In this paper, we study the Maximum lifetime Target Coverage problem (MTC), which is to maximize the network lifetime while guaranteeing the complete coverage of all the targets. Many centralized algorithms have been proposed to solve this problem. A very few distributed versions have also been pres ..."
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Cited by 5 (0 self)
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In this paper, we study the Maximum lifetime Target Coverage problem (MTC), which is to maximize the network lifetime while guaranteeing the complete coverage of all the targets. Many centralized algorithms have been proposed to solve this problem. A very few distributed versions have also been presented but none of them obtains a good approximation ratio. In this paper, we propose two O(log n) localized algorithms. In particular, we first reduce the MTC problem to the domatic number problem in directed graphs. This relation shows that a feasible solution to the domatic number problem is also a feasible solution to the MTC problem. We next prove the lower and upper bounds of this domatic number. Based on this proof, we present two O(log n)localized algorithms to solve the MTC problem.
A Dominating and Absorbent Set in Wireless Adhoc Networks with Different Transmission
 Range,” Proceedings of the 8th ACM International Symposium on Mobile Ad Hoc Networking and Computing (MOBIHOC
, 2007
"... Unlike a cellular or wired network, there is no base station or network infrastructure in a wireless adhoc network, in which nodes communicate with each other via peer communications. In order to make routing and flooding efficient in such an infrastructureless network, Connected Dominating Set (CD ..."
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Cited by 4 (0 self)
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Unlike a cellular or wired network, there is no base station or network infrastructure in a wireless adhoc network, in which nodes communicate with each other via peer communications. In order to make routing and flooding efficient in such an infrastructureless network, Connected Dominating Set (CDS) as a virtual backbone has been extensively studied. Most of the existing studies on the CDS problem have focused on unit disk graphs, where every node in a network has the same transmission range. However, nodes may have different powers due to difference in functionalities, power control, topology control, and so on. In this case, it is desirable to model such a network as a disk graph where each node has different transmission range. In this paper, we define Minimum Strongly Connected Dominating and Absorbent Set (MSCDAS) in a disk graph, which is the counterpart of minimum CDS in unit disk graph. We propose a constant approximation algorithm when the ratio of the maximum to the minimum in transmission range is bounded. We also present two heuristics and compare the performances of the proposed schemes through simulation.