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33
Approximation Algorithms for Connected Dominating Sets
 Algorithmica
, 1996
"... The dominating set problem in graphs asks for a minimum size subset of vertices with the following property: each vertex is required to either be in the dominating set, or adjacent to some node in the dominating set. We focus on the question of finding a connected dominating set of minimum size, whe ..."
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Cited by 277 (9 self)
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The dominating set problem in graphs asks for a minimum size subset of vertices with the following property: each vertex is required to either be in the dominating set, or adjacent to some node in the dominating set. We focus on the question of finding a connected dominating set of minimum size, where the graph induced by vertices in the dominating set is required to be connected as well. This problem arises in network testing, as well as in wireless communication. Two polynomial time algorithms that achieve approximation factors of O(H (\Delta)) are presented, where \Delta is the maximum degree, and H is the harmonic function. This question also arises in relation to the traveling tourist problem, where one is looking for the shortest tour such that each vertex is either visited, or has at least one of its neighbors visited. We study a generalization of the problem when the vertices have weights, and give an algorithm which achieves a performance ratio of 3 ln n. We also consider the ...
Competitive Paging With Locality of Reference
 Journal of Computer and System Sciences
, 1991
"... Abstract The SleatorTarjan competitive analysis of paging [Comm. of the ACM; 28:202 208, 1985] gives us the ability to make strong theoretical statements about the performance of paging algorithms without making probabilistic assumptions on the input. Nevertheless practitioners voice reservations ..."
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Cited by 121 (3 self)
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Abstract The SleatorTarjan competitive analysis of paging [Comm. of the ACM; 28:202 208, 1985] gives us the ability to make strong theoretical statements about the performance of paging algorithms without making probabilistic assumptions on the input. Nevertheless practitioners voice reservations about the model, citing its inability to discern between LRU and FIFO (algorithms whose performances differ markedly in practice), and the fact that the theoretical competitiveness of LRU is much larger than observed in practice. In addition, we would like to address the following important question: given some knowledge of a program's reference pattern, can we use it to improve paging performance on that program?
2Approximation Algorithm for Finding a Spanning Tree with Maximum Number of Leaves
 Lect. Notes Comput. Sci
, 1998
"... . We study the problem of finding a spanning tree with maximum number of leaves. We present a simple 2approximation algorithm for the problem, improving on the approximation ratio of 3 achieved by the best previous algorithms. We also study the variant in which a given set of vertices must be leave ..."
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Cited by 26 (0 self)
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. We study the problem of finding a spanning tree with maximum number of leaves. We present a simple 2approximation algorithm for the problem, improving on the approximation ratio of 3 achieved by the best previous algorithms. We also study the variant in which a given set of vertices must be leaves of the spanning tree, and we present a 5/2approximation algorithm for this version of the problem. 1 Introduction In this paper we study the problem of finding in a given graph a spanning tree with maximum number of leaves. This problem has applications in the design of communication networks [5], circuit layouts [11], and in distributed systems [10]. Galbiati et. al [3] have proven that the problem is MAX SNPcomplete, and hence that there is no polynomial time approximation scheme for the problem unless P=NP. In this paper we present a 2approximation algorithm for the problem, improving on the previous best performance ratio of 3 achieved by algorithms of Ravi and Lu [8, 9]. We briefl...
Approximating Maximum Leaf Spanning Trees in Almost Linear Time
 Journal of Algorithms
, 1998
"... Given an undirected graph, finding a spanning tree of the graph with maximum number of leaves is MAX SNPcomplete. In this paper we give a new greedy 3approximation algorithm for maximumleaf spanning trees. The running time O((m+n)ff(m; n)) required by our algorithm, where m is the number of ed ..."
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Cited by 25 (0 self)
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Given an undirected graph, finding a spanning tree of the graph with maximum number of leaves is MAX SNPcomplete. In this paper we give a new greedy 3approximation algorithm for maximumleaf spanning trees. The running time O((m+n)ff(m; n)) required by our algorithm, where m is the number of edges and n is the number of nodes, is almost linear in the size of the graph. We also demonstrate that our analysis of the performance of the greedy algorithm is tight via an example. Research supported in part by an NSF CAREER grant CCR9625297. 1 1 Introduction Given a connected undirected graph G = (V; E), the maximum leaf spanning tree problem is to find a spanning tree of G with the maximum number of leaves. This problem finds applications in communication networks and circuit layouts [4, 14]. The maximum leaf spanning tree problem is NPcomplete [7] and MAX SNPcomplete [6]. Previous Work The maximum leaf spanning tree problem has been extensively studied [3, 5, 8, 9, 10, 11, 12...
The Power of Local Optimization: Approximation Algorithms for Maximumleaf Spanning Tree
 In Proceedings, Thirtieth Annual Allerton Conference on Communication, Control and Computing
, 1996
"... Given an undirected graph G, finding a spanning tree of G with maximum number of leaves is NPcomplete. We use the simple technique of local optimization to provide the first approximation algorithms for this problem. Our algorithms run in polynomial time to produce locally optimal solutions. We pro ..."
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Cited by 21 (3 self)
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Given an undirected graph G, finding a spanning tree of G with maximum number of leaves is NPcomplete. We use the simple technique of local optimization to provide the first approximation algorithms for this problem. Our algorithms run in polynomial time to produce locally optimal solutions. We prove that locally optimal solutions to this problem are globally nearoptimal. In particular, we prove that two such algorithms have performance ratios of 5 and 3. The latter algorithm employs more powerful localimprovement steps than the former and hence has higher running time. This may indicate an interesting tradeoff between the performance ratios and the running times of the series of algorithms we describe. Keywords: Approximation algorithms, NPcomplete problems, Performance ratio, Local optimization, Communication network design, Combinatorial algorithms. 1 Introduction Given an undirected graph G = (V; E), the Maximum Leaf Spanning Tree problem is to find a spanning tree of G with ...
Hardness and approximation results for black hole search in arbitrary graphs
 In Proc. 12th Coll. on Structural Information and Communication complexity (SIROCCO’05
, 2005
"... Abstract. A black hole is a highly harmful stationary process residing in a node of a network and destroying all mobile agents visiting the node, without leaving any trace. We consider the task of locating a black hole in a (partially) synchronous arbitrary network, assuming an upper bound on the ti ..."
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Cited by 19 (5 self)
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Abstract. A black hole is a highly harmful stationary process residing in a node of a network and destroying all mobile agents visiting the node, without leaving any trace. We consider the task of locating a black hole in a (partially) synchronous arbitrary network, assuming an upper bound on the time of any edge traversal by an agent. For a given graph and a given starting node we are interested in finding the fastest possible Black Hole Search by two agents (the minimum number of agents capable to identify a black hole). We prove that this problem is NPhard in arbitrary graphs, thus solving an open problem stated in [2]. We also give a 7/2approximation algorithm, thus improving on the 4approximation scheme observed in [2]. Our approach is to explore the given input graph via some spanning tree. Even if it represents a very natural technique, we prove that this approach cannot achieve an approximation ratio better than 3/2.
Connected Domination and Spanning Trees with Many Leaves
 SIAM J. Discrete Math
, 2000
"... Abstract Let G = (V; E) be a connected graph. A connected dominating set S ae V is a dominating set that induces a connected subgraph of G. The connected domination number of G, denoted fl ..."
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Cited by 15 (2 self)
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Abstract Let G = (V; E) be a connected graph. A connected dominating set S ae V is a dominating set that induces a connected subgraph of G. The connected domination number of G, denoted fl
Pricing strategies for viral marketing on social networks
 In WINE
, 2009
"... We study the use of viral marketing strategies on social networks to maximize revenue from the sale of a single product. We propose a model in which the decision of a buyer to buy the product is influenced by friends that own the product and the price at which the product is offered. The influence m ..."
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Cited by 15 (0 self)
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We study the use of viral marketing strategies on social networks to maximize revenue from the sale of a single product. We propose a model in which the decision of a buyer to buy the product is influenced by friends that own the product and the price at which the product is offered. The influence model we analyze is quite general, naturally extending both the Linear Threshold model and the Independent Cascade model, while also incorporating price information. We consider sales proceeding in a cascading manner through the network, i.e. a buyer is offered the product via recommendations from its neighbors who own the product. In this setting, the seller influences events by offering a cashback to recommenders and by setting prices (via coupons or discounts) for each buyer in the social network. Finding a seller strategy which maximizes the expected revenue in this setting turns out to be NPhard. However, we propose a seller strategy that generates revenue guaranteed to be within a constant factor of the optimal strategy in a wide variety of models. The strategy is based on an influenceandexploit idea, and it consists of finding the right tradeoff at each time step between: generating revenue from the current user versus offering the product for free and using the influence generated from this sale later in the process. We also show how local search can be used to improve the performance of this technique in practice. 1
Parameterized Algorithms for Directed Maximum Leaf Problems
 Proc. ICALP 2007, LNCS 4596
, 2007
"... Abstract. We prove that finding a rooted subtree with at least k leaves in a digraph is a fixed parameter tractable problem. A similar result holds for finding rooted spanning trees with many leaves in digraphs from a wide family L that includes all strong and acyclic digraphs. This settles complete ..."
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Cited by 12 (7 self)
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Abstract. We prove that finding a rooted subtree with at least k leaves in a digraph is a fixed parameter tractable problem. A similar result holds for finding rooted spanning trees with many leaves in digraphs from a wide family L that includes all strong and acyclic digraphs. This settles completely an open question of Fellows and solves another one for digraphs in L. Our algorithms are based on the following combinatorial result which can be viewed as a generalization of many results for a ‘spanning tree with many leaves ’ in the undirected case, and which is interesting on its own: If a digraph D ∈ L of order n with minimum indegree at least 3 contains a rooted spanning tree, then D contains one with at least (n/2) 1/5 − 1 leaves. 1
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 12 (1 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.