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23
Incremental Clustering and Dynamic Information Retrieval
, 1997
"... Motivated by applications such as document and image classification in information retrieval, we consider the problem of clustering dynamic point sets in a metric space. We propose a model called incremental clustering which is based on a careful analysis of the requirements of the information retri ..."
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Cited by 186 (4 self)
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Motivated by applications such as document and image classification in information retrieval, we consider the problem of clustering dynamic point sets in a metric space. We propose a model called incremental clustering which is based on a careful analysis of the requirements of the information retrieval application, and which should also be useful in other applications. The goal is to efficiently maintain clusters of small diameter as new points are inserted. We analyze several natural greedy algorithms and demonstrate that they perform poorly. We propose new deterministic and randomized incremental clustering algorithms which have a provably good performance. We complement our positive results with lower bounds on the performance of incremental algorithms. Finally, we consider the dual clustering problem where the clusters are of fixed diameter, and the goal is to minimize the number of clusters.
Analysis of a local search heuristic for facility location problems
 IN PROCEEDINGS OF THE 9TH ANNUAL ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS
, 1998
"... In this paper, we study approximation algorithms for several NPhard facility location problems. We prove that a simple local search heuristic yields polynomialtime constantfactor approximation bounds for the metric versions of the uncapacitated kmedian problem and the uncapacitated facility loca ..."
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Cited by 159 (4 self)
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In this paper, we study approximation algorithms for several NPhard facility location problems. We prove that a simple local search heuristic yields polynomialtime constantfactor approximation bounds for the metric versions of the uncapacitated kmedian problem and the uncapacitated facility location problem. (For the kmedian problem, our algorithms require a constantfactor blowup in the parameter k.) This local search heuristic was rst proposed several decades ago, and has been shown to exhibit good practical performance in empirical studies. We also extend the above results to obtain constantfactor approximation bounds for the metric versions of capacitated kmedian and facility location problems.
Parameterized Complexity: A Framework for Systematically Confronting Computational Intractability
 DIMACS Series in Discrete Mathematics and Theoretical Computer Science
, 1997
"... In this paper we give a programmatic overview of parameterized computational complexity in the broad context of the problem of coping with computational intractability. We give some examples of how fixedparameter tractability techniques can deliver practical algorithms in two different ways: (1) by ..."
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Cited by 86 (16 self)
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In this paper we give a programmatic overview of parameterized computational complexity in the broad context of the problem of coping with computational intractability. We give some examples of how fixedparameter tractability techniques can deliver practical algorithms in two different ways: (1) by providing useful exact algorithms for small parameter ranges, and (2) by providing guidance in the design of heuristic algorithms. In particular, we describe an improved FPT kernelization algorithm for Vertex Cover, a practical FPT algorithm for the Maximum Agreement Subtree (MAST) problem parameterized by the number of species to be deleted, and new general heuristics for these problems based on FPT techniques. In the course of making this overview, we also investigate some structural and hardness issues. We prove that an important naturally parameterized problem in artificial intelligence, STRIPS Planning (where the parameter is the size of the plan) is complete for W [1]. As a corollary, this implies that kStep Reachability for Petri Nets is complete for W [1]. We describe how the concept of treewidth can be applied to STRIPS Planning and other problems of logic to obtain FPT results. We describe a surprising structural result concerning the top end of the parameterized complexity hierarchy: the naturally parameterized Graph kColoring problem cannot be resolved with respect to XP either by showing membership in XP, or by showing hardness for XP without settling the P = NP question one way or the other.
On Enumerating All Minimal Solutions of Feedback Problems
"... We present an alg orithm thatg enerates all (inclusionwise) minimal feedback vertex sets of a directedg raph G =(V,E). The feedback vertex sets of G areg enerated with a polynomial delay of O # V  2 (V  + E) # . We further show that the underlying technique can be tailored tog enerate all ..."
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Cited by 19 (0 self)
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We present an alg orithm thatg enerates all (inclusionwise) minimal feedback vertex sets of a directedg raph G =(V,E). The feedback vertex sets of G areg enerated with a polynomial delay of O # V  2 (V  + E) # . We further show that the underlying technique can be tailored tog enerate all minimal solutions for the undirected case and the directed feedback arc set problem, both with a polynomial delay of O # V E (V  + E) # . Finally we prove that computing the number of minimal feedback arc sets is #Phard.
Fully Polynomial Time Approximation Schemes for Stochastic Dynamic Programs
, 2008
"... We develop a framework for obtaining Fully Polynomial Time Approximation Schemes (FPTASs) for stochastic univariate dynamic programs with either convex or monotone singleperiod cost functions. Using our framework, we give the first FPTASs for several NPhard problems in various fields of research s ..."
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Cited by 16 (0 self)
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We develop a framework for obtaining Fully Polynomial Time Approximation Schemes (FPTASs) for stochastic univariate dynamic programs with either convex or monotone singleperiod cost functions. Using our framework, we give the first FPTASs for several NPhard problems in various fields of research such as knapsackrelated problems, logistics, operations management, economics, and mathematical finance.
Packing and covering δhyperbolic spaces by balls
 In APPROXRANDOM 2007
"... Abstract. We consider the problem of covering and packing subsets of δhyperbolic metric spaces and graphs by balls. These spaces, defined via a combinatorial Gromov condition, have recently become of interest in several domains of computer science. Specifically, given a subset S of a δhyperbolic gr ..."
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Cited by 10 (3 self)
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Abstract. We consider the problem of covering and packing subsets of δhyperbolic metric spaces and graphs by balls. These spaces, defined via a combinatorial Gromov condition, have recently become of interest in several domains of computer science. Specifically, given a subset S of a δhyperbolic graph G and a positive number R, let γ(S, R) be the minimum number of balls of radius R covering S. It is known that computing γ(S, R) or approximating this number within a constant factor is hard even for 2hyperbolic graphs. In this paper, using a primaldual approach, we show how to construct in polynomial time a covering of S with at most γ(S, R) balls of (slightly larger) radius R + δ. This result is established in the general framework of δhyperbolic geodesic metric spaces and is extended to some other set families derived from balls. This covering algorithm is used to design better than in general case approximation algorithms for the augmentation problem of δhyperbolic graphs with diameter constraints and slackness δ and for the kcenter problem in δhyperbolic graphs. 1
Minimizing Wirelength in Zero and Bounded Skew Clock Trees
, 1999
"... An important problem in VLSI design is distributing a clock signal to synchronous elements in aVLSI circuit so that the signal arrives at all elements simultaneously. The signal is distributed by means of a clock routing tree rooted at a global clock source. The difference in length between the long ..."
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Cited by 7 (0 self)
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An important problem in VLSI design is distributing a clock signal to synchronous elements in aVLSI circuit so that the signal arrives at all elements simultaneously. The signal is distributed by means of a clock routing tree rooted at a global clock source. The difference in length between the longest and shortest rootleaf path is called the skew of the tree. The problem is to construct a clock tree with zero skew (to achieve synchronicity) and minimal sum of edge lengths (so that circuit area and clock tree capacitance are minimized). We give the first constantfactor approximation algorithms for this problem and its variants that arise in the VLSI context. For the zero skew problem in general metric spaces, we give an approximation
On Computing All Minimal Solutions for Feedback Problems
, 1997
"... We present an algorithm that generates all (inclusionwise) minimal feedback vertex sets of a directed graph G = (V; E). The feedback vertex sets of G are generated with a polynomial delay of O \Gamma jV j 2 (jV j + jEj) \Delta . Variants of the algorithm generate all minimal solutions for th ..."
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Cited by 4 (0 self)
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We present an algorithm that generates all (inclusionwise) minimal feedback vertex sets of a directed graph G = (V; E). The feedback vertex sets of G are generated with a polynomial delay of O \Gamma jV j 2 (jV j + jEj) \Delta . Variants of the algorithm generate all minimal solutions for the undirected case and the directed feedback arc set problem, both with a polynomial delay of O \Gamma jV j jEj (jV j + jEj) \Delta .
Solving the feedback vertex set problem on undirected graphs
 DISCRETE APPLIED MATHEMATICS
, 1999
"... Feedback problems consist of removing a minimal number of vertices of a directed or undirected graph in order to make it acyclic. The problem is known to be NPcomplete. In this paper we consider the variant on undirected graphs. The polyhedral structure of the Feedback Vertex Set polytope is studie ..."
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Cited by 4 (0 self)
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Feedback problems consist of removing a minimal number of vertices of a directed or undirected graph in order to make it acyclic. The problem is known to be NPcomplete. In this paper we consider the variant on undirected graphs. The polyhedral structure of the Feedback Vertex Set polytope is studied. We prove that this polytope is full dimensional and show that some inequalities are facet defining. We describe a new large class of valid constraints, the subset inequalities. A branchandcut algorithm for the exact solution of the problem is then outlined, and separation algorithms for the inequalities studied in the paper are proposed. A Local Search heuristic is described next. Finally we create a library of 1400 random generated instances with the geometric structure suggested by the applications, and we computationally compare the two algorithmic approaches on our library.