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61
A unified approach to approximating resource allocation and scheduling
 Journal of the ACM
, 2000
"... We present a general framework for solving resource allocation and scheduling problems. Given a resource of fixed size, we present algorithms that approximate the maximum throughput or the minimum loss by a constant factor. Our approximation factors apply to many problems, among which are: (i) real ..."
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Cited by 156 (23 self)
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We present a general framework for solving resource allocation and scheduling problems. Given a resource of fixed size, we present algorithms that approximate the maximum throughput or the minimum loss by a constant factor. Our approximation factors apply to many problems, among which are: (i) realtime scheduling of jobs on parallel machines, (ii) bandwidth allocation for sessions between two endpoints, (iii) general caching, (iv) dynamic storage allocation, and (v) bandwidth allocation on optical line and ring topologies. For some of these problems we provide the first constant factor approximation algorithm. Our algorithms are simple and efficient and are based on the localratio technique. We note that they can equivalently be interpreted within the primaldual schema.
The primaldual method for approximation algorithms and its application to network design problems.
, 1997
"... Abstract In this survey, we give an overview of a technique used to design and analyze algorithms that provide approximate solutions to N P hard problems in combinatorial optimization. Because of parallels with the primaldual method commonly used in combinatorial optimization, we call it the prim ..."
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Cited by 137 (5 self)
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Abstract In this survey, we give an overview of a technique used to design and analyze algorithms that provide approximate solutions to N P hard problems in combinatorial optimization. Because of parallels with the primaldual method commonly used in combinatorial optimization, we call it the primaldual method for approximation algorithms. We show how this technique can be used to derive approximation algorithms for a number of different problems, including network design problems, feedback vertex set problems, and facility location problems.
Local Ratio: A Unified Framework for Approximation Algorithms
 ACM Computing Surveys
, 2004
"... ..."
On the equivalence between the primaldual schema and the local ratio technique
 In 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX). Number 2129 in Lecture Notes in Computer Science
, 2001
"... Abstract. We discuss two approximation paradigms that were used to construct many approximation algorithms during the last two decades, the primaldual schema and the local ratio technique. Recently, primaldual algorithms were devised by first constructing a local ratio algorithm and then transform ..."
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Cited by 31 (8 self)
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Abstract. We discuss two approximation paradigms that were used to construct many approximation algorithms during the last two decades, the primaldual schema and the local ratio technique. Recently, primaldual algorithms were devised by first constructing a local ratio algorithm and then transforming it into a primaldual algorithm. This was done in the case of the 2approximation algorithms for the feedback vertex set problem and in the case of the first primaldual algorithms for maximization problems. Subsequently, the nature of the connection between the two paradigms was posed as an open question by Williamson [Math. Program., 91 (2002), pp. 447–478]. In this paper we answer this question by showing that the two paradigms are equivalent.
Opportunity Cost Algorithms for Combinatorial Auctions
 In Erricos John Kontoghiorghes, Berç Rustem, and Stavros Siokos, editors, Applied Optimization: Computational Methods in DecisionMaking, Economics and Finance
, 2000
"... Two general algorithms based on opportunity costs are given for approximating a revenue maximizing set of bids an auctioneer should accept, in a combinatorial auction in which each bidder offers a price for some subset of the available goods and the auctioneer can only accept nonintersecting bids. ..."
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Cited by 21 (2 self)
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Two general algorithms based on opportunity costs are given for approximating a revenue maximizing set of bids an auctioneer should accept, in a combinatorial auction in which each bidder offers a price for some subset of the available goods and the auctioneer can only accept nonintersecting bids. Since this problem is difficult even to approximate in general, the algorithms are most useful when the bids are restricted to be connected node subsets of an underlying object graph that represents which objects are relevant to each other. The approximation ratios of the algorithms depend on structural properties of this graph and are small constants for many interesting families of object graphs. The running times of the algorithms are linear in the size of the bid graph, which describes the conflicts between bids. Extensions of the algorithms allow for efficient processing of additional constraints, such as budget constraints that associate bids with particular bidders and limit how many bids from a particular bidder can be accepted.
Efficient approximation of convex recolorings
 In Proceedings APPROX 2005: 8th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, published with Proceedings RANDOM 2005
, 2005
"... A coloring of a tree is convex if the vertices that pertain to any color induce a connected subtree; a partial coloring (which assigns colors to some of the vertices) is convex if it can be completed to a convex (total) coloring. Convex coloring of trees arises in areas such as phylogenetics, lingui ..."
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Cited by 18 (2 self)
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A coloring of a tree is convex if the vertices that pertain to any color induce a connected subtree; a partial coloring (which assigns colors to some of the vertices) is convex if it can be completed to a convex (total) coloring. Convex coloring of trees arises in areas such as phylogenetics, linguistics, etc. e.g., a perfect phylogenetic tree is one in which the states of each character induce a convex coloring of the tree. Research on perfect phylogeny is usually focused on finding a tree so that few predetermined partial colorings of its vertices are convex. When a coloring of a tree is not convex, it is desirable to know ”how far ” it is from a convex one. In [18], a natural measure for this distance, called the recoloring distance was defined: the minimal number of color changes at the vertices needed to make the coloring convex. This can be viewed as minimizing the number of “exceptional vertices ” w.r.t. to a closest convex coloring. The problem was proved to be NPhard even for colored strings. In this paper we continue the work of [18], and present a 2approximation algorithm of convex recoloring of strings whose running time O(cn), where c is the number of colors and n is the size of the input, and an O(cn 2) 3approximation algorithm for convex recoloring of trees. ∗ A preliminary version of the results in this paper appeared in [19].
Approximating the 2interval pattern problem
 IN PROCEEDINGS OF THE 13TH ANNUAL EUROPEAN SYMPOSIUM ON ALGORITHMS (ESA
, 2005
"... We address the problem of approximating the 2Interval Pattern problem over its various models and restrictions. This problem, which is motivated by RNA secondary structure prediction, asks to find a maximum cardinality subset of a 2interval set with respect to some prespecified model. For each s ..."
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Cited by 15 (6 self)
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We address the problem of approximating the 2Interval Pattern problem over its various models and restrictions. This problem, which is motivated by RNA secondary structure prediction, asks to find a maximum cardinality subset of a 2interval set with respect to some prespecified model. For each such model, we give varying approximation quality depending on the different possible restrictions imposed on the input 2interval set.
RECONFIGURATIONS IN GRAPHS AND GRIDS
, 2006
"... Let G be a connected graph, and let V and V′ two nelement subsets of its vertex set V (G). Imagine that we place a chip at each element of V and we want to move them into the positions of V ′ (V and V′ may have common elements). A move is defined as shifting a chip from v1 to v2 (v1, v2 ∈ V (G)) on ..."
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Cited by 12 (4 self)
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Let G be a connected graph, and let V and V′ two nelement subsets of its vertex set V (G). Imagine that we place a chip at each element of V and we want to move them into the positions of V ′ (V and V′ may have common elements). A move is defined as shifting a chip from v1 to v2 (v1, v2 ∈ V (G)) on a path formed by edges of G so that no intermediate vertices are occupied. We give upper and lower bounds on the number of moves that are necessary, and analyze the computational complexity of this problem under various assumptions: labeled versus unlabeled chips, arbitrary graphs versus the case when the graph is the rectangular (infinite) planar grid, etc. We prove hardness and inapproximability results for several variants of the problem. We also give a lineartime algorithm which performs an optimal (minimum) number of moves for the unlabeled version in a tree, and a constantratio approximation algorithm for the unlabeled version in a graph. The graph algorithm uses the tree algorithm as a subroutine.
Combinatorial Algorithms for Feedback Problems in Directed Graphs
 Inf. Process. Lett
, 2003
"... Given a weighted directed graph G = (V, A), the minimum feedback arc set problem consists of finding a minimum weight set of arcs A # A such that the directed graph A # ) is acyclic. Similarly, the minimum feedback vertex set problem consists of finding a minimum weight set of vertices containi ..."
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Cited by 12 (1 self)
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Given a weighted directed graph G = (V, A), the minimum feedback arc set problem consists of finding a minimum weight set of arcs A # A such that the directed graph A # ) is acyclic. Similarly, the minimum feedback vertex set problem consists of finding a minimum weight set of vertices containing at least one vertex for each directed cycle. Both problems are NPcomplete. We present simple combinatorial algorithms for these problems that achieve an approximation ratio bounded by the length, in terms of number of arcs, of a longest simple cycle of the digraph.
A new lineartime heuristic algorithm for computing the parsimony score of phylogenetic networks: Theoretical bounds and empirical performance
, 2007
"... Phylogenies play a major role in representing the interrelationships among biological entities. Many methods for reconstructing and studying such phylogenies have been proposed, almost all of which assume that the underlying history of a given set of species can be represented by a binary tree. Al ..."
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Cited by 11 (5 self)
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Phylogenies play a major role in representing the interrelationships among biological entities. Many methods for reconstructing and studying such phylogenies have been proposed, almost all of which assume that the underlying history of a given set of species can be represented by a binary tree. Although many biological processes can be effectively modeled and summarized in this fashion, others cannot: recombination, hybrid speciation, and horizontal gene transfer result in networks, rather than trees, of relationships. In a series of papers, we have extended the maximum parsimony (MP) criterion to phylogenetic networks, demonstrated its appropriateness, and established the intractability of the problem of scoring the parsimony of a phylogenetic network. In this work we show the hardness of approximation for the general case of the problem, devise a very fast (lineartime) heuristic algorithm for it, and implement it on simulated as well as biological data.