Results 1  10
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13
Modelbased overlapping clustering
 In KDD
, 2005
"... While the vast majority of clustering algorithms are partitional, many real world datasets have inherently overlapping clusters. Several approaches to finding overlapping clusters have come from work on analysis of biological datasets. In this paper, we interpret an overlapping clustering model prop ..."
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Cited by 29 (6 self)
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While the vast majority of clustering algorithms are partitional, many real world datasets have inherently overlapping clusters. Several approaches to finding overlapping clusters have come from work on analysis of biological datasets. In this paper, we interpret an overlapping clustering model proposed by Segal et al. [23] as a generalization of Gaussian mixture models, and we extend it to an overlapping clustering model based on mixtures of any regular exponential family distribution and the corresponding Bregman divergence. We provide the necessary algorithm modifications for this extension, and present results on synthetic data as well as subsets of 20Newsgroups and EachMovie datasets.
Toward a model for backtracking and dynamic programming
 Comput. Compl
"... We propose a model called priority branching trees (pBT) for backtracking and dynamic programming algorithms. Our model generalizes both the priority model of Borodin, Nielson and Rackoff, as well as a simple dynamic programming model due to Woeginger, and hence spans a wide spectrum of algorithms. ..."
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Cited by 25 (7 self)
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We propose a model called priority branching trees (pBT) for backtracking and dynamic programming algorithms. Our model generalizes both the priority model of Borodin, Nielson and Rackoff, as well as a simple dynamic programming model due to Woeginger, and hence spans a wide spectrum of algorithms. After witnessing the strength of the model, we then show its limitations by providing lower bounds for algorithms in this model for several classical problems such as Interval Scheduling, Knapsack and Satisfiability.
A Class of Hard Small 01 Programs
 INFORMS Journal on Computing
, 1998
"... . In this paper, we consider a class of 01 programs which, although innocent looking, is a challenge for existing solution methods. Solving even small instances from this class is extremely di#cult for conventional branchandbound or branchandcut algorithms. We also experimented with basis redu ..."
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Cited by 22 (2 self)
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. In this paper, we consider a class of 01 programs which, although innocent looking, is a challenge for existing solution methods. Solving even small instances from this class is extremely di#cult for conventional branchandbound or branchandcut algorithms. We also experimented with basis reduction algorithms and with dynamic programming without much success. The paper then examines the performance of two other methods: a group relaxation for 0,1 programs, and a sortingbased procedure following an idea of Wolsey. Although the results with these two methods are somewhat better than with the other four when it comes to checking feasibility, we o#er this class of small 0,1 programs as a challenge to the research community. As of yet, instances from this class with as few as seven constraints and sixty 01 variables are unsolved. 1 Introduction Goal programming [2] is a useful model when a decision maker wants to come "as close as possible" to satisfying a number of incompatible go...
Generalized Knapsack Solvers for MultiUnit Combinatorial Auctions: Analysis and Application to Computational Resource Allocation
 In Workshop on Agent Mediated Electronic Commerce VI: Theories for and Engineering of Distributed Mechanisms and Systems
, 2004
"... The problem of allocating discrete computational resources motivates interest in general multiunit combinatorial exchanges. This paper considers the problem of computing optimal (surplusmaximizing) allocations, assuming unrestricted quasilinear preferences. We present a solver whose pseudopol ..."
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Cited by 17 (3 self)
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The problem of allocating discrete computational resources motivates interest in general multiunit combinatorial exchanges. This paper considers the problem of computing optimal (surplusmaximizing) allocations, assuming unrestricted quasilinear preferences. We present a solver whose pseudopolynomial time and memory requirements are linear in three of four natural measures of problem size: number of agents, length of bids, and units of each resource. In applications where the number of resource types is inherently a small constant, e.g., computational resource allocation, such a solver offers advantages over more elaborate approaches developed for highdimensional problems.
How well can PrimalDual and LocalRatio algorithms perform?
, 2007
"... We define an algorithmic paradigm, the stack model, that captures many primaldual and localratio algorithms for approximating covering and packing problems. The stack model is defined syntactically and without any complexity limitations and hence our approximation bounds are independent of the P v ..."
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Cited by 10 (4 self)
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We define an algorithmic paradigm, the stack model, that captures many primaldual and localratio algorithms for approximating covering and packing problems. The stack model is defined syntactically and without any complexity limitations and hence our approximation bounds are independent of the P vs NP question. We provide tools to bound the performance of primal dual and local ratio algorithms and supply a (log n + 1)/2 inapproximability result for set cover, a 4/3 inapproximability for min steiner tree, and a 0.913 inapproximability for interval scheduling on two machines.
Column basis reduction and decomposable knapsack problems
 Discrete Optimization
"... We propose a very simple preconditioning method for integer programming feasibility problems: replacing the problem b ′ ≤ Ax ≤ b x ∈ Zn with b ′ ≤ (AU)y ≤ b y ∈ Zn, where U is a unimodular matrix computed via basis reduction, to make the columns of AU short (i.e., have small Euclidean norm), and n ..."
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Cited by 8 (4 self)
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We propose a very simple preconditioning method for integer programming feasibility problems: replacing the problem b ′ ≤ Ax ≤ b x ∈ Zn with b ′ ≤ (AU)y ≤ b y ∈ Zn, where U is a unimodular matrix computed via basis reduction, to make the columns of AU short (i.e., have small Euclidean norm), and nearly orthogonal (see e.g., [26], [25]). Our approach is termed column basis reduction, and the reformulation is called rangespace reformulation. It is motivated by the technique proposed for equality constrained IPs by Aardal, Hurkens and Lenstra. We also propose a simplified method to compute their reformulation. We also study a family of IP instances, called decomposable knapsack problems (DKPs). DKPs generalize the instances proposed by Jeroslow, Chvátal and Todd, Avis, Aardal and Lenstra, and Cornuéjols et al. They are knapsack problems with a constraint vector of the form pM + r, with p> 0 and r integral vectors, and M a large integer. If the parameters are suitably chosen in DKPs, we prove • hardness results, when branchandbound branching on individual variables is applied; • that they are easy, if one branches on the constraint px instead; and • that branching on the last few variables in either the rangespace or the AHL reformulations is equivalent to branching on px in the original problem. We also provide recipes to generate such instances. Our computational study confirms that the behavior of the studied instances in practice is as predicted by the theory.
An Optimal AlgoTechCuit for the Knapsack Problem
 IN PROC. INTERNATIONAL CONFERENCE ON APPLICATIONSPECIFIC ARRAY PROCESSORS  ASAP'93
, 1994
"... We present a formal derivation and proof of correctness of a systolic array for the knapsack problem, a well known, NPcomplete problem. The dependency graph of the algorithm is not completely known statically, so the derivation also serves as a case study for systolic synthesis for this class of p ..."
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Cited by 7 (6 self)
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We present a formal derivation and proof of correctness of a systolic array for the knapsack problem, a well known, NPcomplete problem. The dependency graph of the algorithm is not completely known statically, so the derivation also serves as a case study for systolic synthesis for this class of programs. The array is itself important since it achieves optimal performance on a model much weaker than a PRAM (ring of PE's with a fixed size memory and only nearest neighbor interconnections). We show how the memory size of each PE can be chosen so that the running time is minimized by formulating and solving a non linear optimization problem. For this, we use the expected running time as the cost function and a register level model of VLSI. The original array has an intricate tagbased control mechanism which is difficult to implement. We show how this can be reduced to two simple counters and a few flipflops. Coefficient loading is done with a multirate clock which avoids the need ...
Locally vs. Globally Optimized FlowBased Content Distribution to Mobile Nodes
"... Abstract—The paper deals with efficient distribution of timely information to flows of mobile devices. We consider the case where a set of Information Dissemination Devices (IDDs) broadcast a limited amount of information to passing mobile nodes that are moving along welldefined paths. This is the ..."
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Cited by 3 (1 self)
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Abstract—The paper deals with efficient distribution of timely information to flows of mobile devices. We consider the case where a set of Information Dissemination Devices (IDDs) broadcast a limited amount of information to passing mobile nodes that are moving along welldefined paths. This is the case, for example, in intelligent transportation systems. We develop a novel model that captures the main aspects of the problem, and define a new optimization problem we call MBMAP (Maximum Benefit Message Assignment Problem). We study the computational complexity of this problem in the global and local cases, and provide new approximation algorithms. I.
Simple Lifted Cover Inequalities and Hard Knapsack Problems
, 2004
"... We consider a class of random knapsack instances described by Chvátal, who showed that with probability going to 1, such instances require an exponential number of branchandbound nodes. We show that even with the use of simple lifted cover inequalities, an exponential number of nodes is required w ..."
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Cited by 1 (0 self)
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We consider a class of random knapsack instances described by Chvátal, who showed that with probability going to 1, such instances require an exponential number of branchandbound nodes. We show that even with the use of simple lifted cover inequalities, an exponential number of nodes is required with probability going to 1. It is not surprising that there exist integer programming (IP) instances for which solution by branchandbound requires an exponential number of nodes, since integer programming is an NPcomplete problem while the linear programs solved at each branchandbound node are polynomially solvable. Examples of such instances were given by Jeroslow [5], who presented a set of simple instances of the knapsack problem which require an exponential number of branchandbound nodes when branching on variables, and by Chvátal [1], who considered a class of random instances of the knapsack problem and showed that with probability converging to 1, such a random instance requires exponentially many branchandbound nodes to solve. Most modern IP solvers use branchandcut algorithms, which combine branchandbound with the use of cutting planes. Gu, Nemhauser, and Savelsbergh [4] considered solving the knapsack problem with branchandcut. They presented a set of instances that require an exponential number of branchandbound nodes even with the addition of simple lifted cover inequalities. More recent work in proving exponential worstcase bounds in the presence of various cutting planes has been done by Dash [2], who proved worstcase exponential bounds in the presence of liftandproject cuts, ChvátalGomory inequalities, and matrix cuts as described by Lovász and Schrijver. The work of Gu et al. and Dash is similar to Jeroslow’s work in that specific “worstcase ” examples are presented. In this paper we build on Chvátal’s results, which are concerned with averagecase performance over a class of random instances. We add all simple lifted cover inequalities to his formulation and show that an exponential number of branchandbound nodes is required with probability converging to 1. This result is not suggested by the NPhardness of binary knapsack problems, because cover inequality separation for these problems is NPhard [6]. 1
HEURISTICS FOR INTEGER PROGRAMS
"... Permission is hereby granted to the University of Alberta Library to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. The author reserves all other publication and other rights in association with the copyright in the ..."
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Permission is hereby granted to the University of Alberta Library to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. The author reserves all other publication and other rights in association with the copyright in the thesis, and except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatever without the author’s prior written permission.