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33
Fast Approximation Algorithms for Fractional Packing and Covering Problems
, 1995
"... This paper presents fast algorithms that find approximate solutions for a general class of problems, which we call fractional packing and covering problems. The only previously known algorithms for solving these problems are based on general linear programming techniques. The techniques developed ..."
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Cited by 232 (14 self)
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This paper presents fast algorithms that find approximate solutions for a general class of problems, which we call fractional packing and covering problems. The only previously known algorithms for solving these problems are based on general linear programming techniques. The techniques developed in this paper greatly outperform the general methods in many applications, and are extensions of a method previously applied to find approximate solutions to multicommodity flow problems. Our algorithm is a Lagrangean relaxation technique; an important aspect of our results is that we obtain a theoretical analysis of the running time of a Lagrangean relaxationbased algorithm. We give several applications of our algorithms. The new approach yields several orders of magnitude of improvement over the best previously known running times for algorithms for the scheduling of unrelated parallel machines in both the preemptive and the nonpreemptive models, for the job shop problem, for th...
ExternalMemory Computational Geometry
, 1993
"... In this paper, we give new techniques for designing efficient algorithms for computational geometry problems that are too large to be solved in internal memory, and we use these techniques to develop optimal and practical algorithms for a number of important largescale problems. We discuss our algor ..."
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Cited by 121 (20 self)
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In this paper, we give new techniques for designing efficient algorithms for computational geometry problems that are too large to be solved in internal memory, and we use these techniques to develop optimal and practical algorithms for a number of important largescale problems. We discuss our algorithms primarily in the contex't of single processor/single disk machines, a domain in which they are not only the first known optimal results but also of tremendous practical value. Our methods also produce the first known optimal algorithms for a wide range of twolevel and hierarchical muir{level memory models, including parallel models. The algorithms are optimal both in terms of I/0 cost and internal computation.
A Functional Approach to External Graph Algorithms
 Algorithmica
, 1998
"... . We present a new approach for designing external graph algorithms and use it to design simple external algorithms for computing connected components, minimum spanning trees, bottleneck minimum spanning trees, and maximal matchings in undirected graphs and multigraphs. Our I/O bounds compete w ..."
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Cited by 90 (2 self)
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. We present a new approach for designing external graph algorithms and use it to design simple external algorithms for computing connected components, minimum spanning trees, bottleneck minimum spanning trees, and maximal matchings in undirected graphs and multigraphs. Our I/O bounds compete with those of previous approaches. Unlike previous approaches, ours is purely functionalwithout side effectsand is thus amenable to standard checkpointing and programming language optimization techniques. This is an important practical consideration for applications that may take hours to run. 1 Introduction We present a divideandconquer approach for designing external graph algorithms, i.e., algorithms on graphs that are too large to fit in main memory. Our approach is simple to describe and implement: it builds a succession of graph transformations that reduce to sorting, selection, and a recursive bucketing technique. No sophisticated data structures are needed. We apply our t...
Efficient Routing in Networks with Long Range Contacts (Extended Abstract)
, 2001
"... Lali Barri`ere , Pierre Fraigniaud , Evangelos Kranakis , and Danny Krizanc Dept. de Matem`atica Aplicada i Telem`atica, Universitat Polit`ecnica de Catalunya. ..."
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Cited by 80 (14 self)
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Lali Barri`ere , Pierre Fraigniaud , Evangelos Kranakis , and Danny Krizanc Dept. de Matem`atica Aplicada i Telem`atica, Universitat Polit`ecnica de Catalunya.
Adding Multiple Cost Constraints to Combinatorial Optimization Problems, with Applications to Multicommodity Flows
 IN PROCEEDINGS OF THE 27TH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING
, 1995
"... Minimum cost multicommodity flow is an instance of a simpler problem (multicommodity flow) to which a cost constraint has been added. In this paper we present a general scheme for solving a large class of such "costadded" problemseven if more than one cost is added. One of the main applicatio ..."
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Cited by 45 (5 self)
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Minimum cost multicommodity flow is an instance of a simpler problem (multicommodity flow) to which a cost constraint has been added. In this paper we present a general scheme for solving a large class of such "costadded" problemseven if more than one cost is added. One of the main applications of this method is a new deterministic algorithm for approximately solving the minimumcost multicommodity flow problem. Our algorithm finds a (1 + ffl) approximation to the minimum cost flow in ~ O(ffl \Gamma3 kmn) time, where k is the number of commodities, m is the number of edges, and n is the number vertices in the input problem. This improves the previous best deterministic bounds of O(ffl \Gamma4 kmn 2 ) [9] and ~ O(ffl \Gamma2 k 2 m 2 ) [15] by factors of n=ffl and fflkm=n respectively. In fact, it even dominates the best randomized bound of ~ O(ffl \Gamma2 km 2 ) [15]. The algorithm presented in this paper efficiently solves several other interesting generali...
Randomly Fallible Teachers: Learning Monotone DNF with an Incomplete Membership Oracle
 Machine Learning
, 1994
"... . We introduce a new faulttolerant model of algorithmic learning using an equivalence oracle and an incomplete membership oracle, in which the answers to a random subset of the learner's membership queries may be missing. We demonstrate that, with high probability, it is still possible to learn mon ..."
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Cited by 27 (5 self)
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. We introduce a new faulttolerant model of algorithmic learning using an equivalence oracle and an incomplete membership oracle, in which the answers to a random subset of the learner's membership queries may be missing. We demonstrate that, with high probability, it is still possible to learn monotone DNF formulas in polynomial time, provided that the fraction of missing answers is bounded by some constant less than one. Even when half the membership queries are expected to yield no information, our algorithm will exactly identify mterm, nvariable monotone DNF formulas with an expected O(mn 2 ) queries. The same task has been shown to require exponential time using equivalence queries alone. We extend the algorithm to handle some onesided errors, and discuss several other possible error models. It is hoped that this work may lead to a better understanding of the power of membership queries and the effects of faulty teachers on query models of concept learning. Keywords: concep...
Random Sampling in Matroids, with Applications to Graph Connectivity and Minimum Spanning Trees
, 1993
"... Random sampling is a powerful way to gather information about a group by considering only a small part of it. We give a paradigm for applying this technique to optimization problems, and demonstrate its effectiveness on matroids. Matroids abstractly model many optimization problems that can be solve ..."
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Cited by 14 (4 self)
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Random sampling is a powerful way to gather information about a group by considering only a small part of it. We give a paradigm for applying this technique to optimization problems, and demonstrate its effectiveness on matroids. Matroids abstractly model many optimization problems that can be solved by greedy methods, such as the minimum spanning tree (MST) problem. Our results have several applications. We give an algorithm that uses simple data structures to construct an MST in O(m+n logn) time (Klein and Tarjan [21] have recently shown that a better choice of parameters makes this algorithm run in O(m + n) time). We give bounds on the connectivity (minimum cut) of a graph suffering random edge failures. We give fast algorithms for packing matroid bases, with particular attention to packing spanning trees in graphs.