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A Model for Minimizing Active Processor Time
"... We introduce the following elementary scheduling problem. We are given a collection of n jobs, where each job Ji has an integer length ℓi as well as a set Ti of time intervals in which it can be feasibly scheduled. Given a parameter B, the processor can schedule up to B jobs at a timeslot t solongas ..."
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We introduce the following elementary scheduling problem. We are given a collection of n jobs, where each job Ji has an integer length ℓi as well as a set Ti of time intervals in which it can be feasibly scheduled. Given a parameter B, the processor can schedule up to B jobs at a timeslot t solongasit is “active”att. The goalis toschedule allthe jobs in the fewestnumber of active timeslots. The machine consumes a fixed amount of energy per active timeslot, regardless of the number of jobs scheduled in that slot (as long as the number of jobs is nonzero). In other words, subject to ℓi units of each job i being scheduled in its feasible region and at each slot at most B jobs being scheduled, we are interested in minimizing the total time during which the machine is active. We present a linear time algorithm for the case where jobs are unit length and each Ti is a single interval. For general Ti, we show that the problem is NPcomplete even for B = 3. However when B = 2, we show that it can be efficiently solved. In addition, we consider a version of the problem where jobs have arbitrary lengths and can be preempted at any point in time. For general B, the problem can be solved by linear programming. For B = 2, the problem amounts to finding a trianglefree 2matching on a special graph. We extend the algorithm of Babenko et. al. [5] to handle our variant, and also to handle nonunit length jobs. This yields an O ( √ Lm) time algorithm to solve the preemptive scheduling problem for B = 2, where L = ∑ iℓi. We alsoshow that for B = 2 and unit length jobs, the optimal nonpreemptive schedule has ≤ 4/3times the activetime of the optimal preemptive schedule; this bound extends to several versions of the problem when jobs have arbitrary length. 1
Achieving anonymity via clustering
 in PODS, 2006
"... Publishing data for analysis from a table containing personal records, while maintaining individual privacy, is a problem of increasing importance today. The traditional approach of deidentifying records is to remove identifying fields such as social security number, name etc. However, recent resea ..."
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Publishing data for analysis from a table containing personal records, while maintaining individual privacy, is a problem of increasing importance today. The traditional approach of deidentifying records is to remove identifying fields such as social security number, name etc. However, recent research has shown that a large fraction of the US population can be identified using nonkey attributes (called quasiidentifiers) such as date of birth, gender, and zip code [15]. Sweeney [16] proposed the kanonymity model for privacy where nonkey attributes that leak information are suppressed or generalized so that, for every record in the modified table, there are at least k−1 other records having exactly the same values for quasiidentifiers. We propose a new method for anonymizing data records, where quasiidentifiers of data records are first clustered and then cluster centers are published. To ensure privacy of the data records, we impose the constraint 1
Diversity Coloring for Distributed Storage in Mobile Networks
, 2001
"... Abstract: Storing multiple copies of files is crucial for ensuring quality of service for data storage in mobile networks. This paper proposes a new scheme, called the KoutofN file distribution scheme, for the placement of files. In this scheme files are splitted, and ReedSolomon codes or other ..."
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Abstract: Storing multiple copies of files is crucial for ensuring quality of service for data storage in mobile networks. This paper proposes a new scheme, called the KoutofN file distribution scheme, for the placement of files. In this scheme files are splitted, and ReedSolomon codes or other maximum distance seperable (MDS) codes are used to produce file segments containing parity information. Multiple copies of the file segments are stored on gateways in the network in such a way that every gateway can retrieve enough file segments from itself and its neighbors within a certain amount of hops for reconstructing the orginal files. The goal is to minimize the maximum number of hops it takes for any gateway to get enough file segments for the file reconstruction. We formulate the KoutofN file distribution scheme as a coloring problem we call diversity coloring. A diversity coloring is defined to be optimal if it uses the smallest number of colors. Upper and lower bounds on the performance of diversity coloring for general graphs are studied. Diversity coloring algorithms for several special classes of graphs—trees, rings and tori—are presented, all of which have linear time complexity. Both the algorithm for trees and the algorithm for rings output optimal diversity colorings. The algorithm for tori guarantees to output optimal diversity coloring when the sizes of tori are sufficiently large. Index Terms: Data storage, diversity coloring, file assignment problem (FAP), graph coloring, KoutofN scheme, maximum distance seperable (MDS) codes, mobile computing, Quality of Service
A Genetic Algorithm Applied to Graph Problems Involving Subsets of Vertices
"... Abstract Many graph problems seek subsets of their vertices that maximize or minimize objective functions on the vertices. Among these are the capacitated pmedian problem, the geometric connected dominating set problem, the capacitated kcenter problem, and the traveling tourist problem. Prior gen ..."
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Abstract Many graph problems seek subsets of their vertices that maximize or minimize objective functions on the vertices. Among these are the capacitated pmedian problem, the geometric connected dominating set problem, the capacitated kcenter problem, and the traveling tourist problem. Prior genetic algorithms research in this area applied a simple mutation of an allele by random replacement. Recently an enhanced operator called hypermutation was developed, proving to be very effective for solving the capacitated pmedian problem. We propose a GA with a new heuristic called the nearest four neighbors heuristic (N4N) for solving graph problems requiring a subset of vertices It is an extension of the hypermutation operator. Genetic algorithms that use each of these three mutation operators (simple, hypermutation, N4N) are applied to instances of the four graphsubset problems listed above. Results show that our N4N heuristic obtained superior results compared to the hypermutation and the simple mutation operators in every test case. I.
The LoadDistance Balancing Problem
"... Problems dealing with assignment of clients to servers have been widely studied. However, they usually do not model the fact that the delay incurred by a client is a function of both the distance to the assigned server and the load on this server, under a given assignment. We study a problem referre ..."
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Problems dealing with assignment of clients to servers have been widely studied. However, they usually do not model the fact that the delay incurred by a client is a function of both the distance to the assigned server and the load on this server, under a given assignment. We study a problem referred to as the LoadDistance Balancing problem (or LDB), where the objective is assigning a set of clients to a set of given servers. Each client suffers a delay that is the sum of the distance to its server and the congestion delay at this server, a nondecreasing function of the number of clients assigned to the server. We address two flavors of LDB – the first one seeking to minimize the maximum incurred delay, and the second one targeted for minimizing the average delay. For the first variation, we present hardness results, a best possible approximation algorithm, and an optimal algorithm for a special case of linear placement of clients and servers. For the second one, an optimal polynomialtime algorithm is presented.
Robust Matchings, Maximum Clustering, and Maximum Capacitated Medians
 in Algorithm Theory  SWAT2000 M. Halld'orsson (Ed.) (Lecture Notes in Computer Science 1851
, 1999
"... We consider complete graphs with nonnegative edge weights. A pmatching is a set of p disjoint edges. We prove the existence of a maximal (with respect to inclusion) matching M that contains for any p jM j p edges whose total weight is at least 1 p 2 of the maximum weight of a pmatching. We us ..."
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We consider complete graphs with nonnegative edge weights. A pmatching is a set of p disjoint edges. We prove the existence of a maximal (with respect to inclusion) matching M that contains for any p jM j p edges whose total weight is at least 1 p 2 of the maximum weight of a pmatching. We use this property to approximate two graph partitioning problems in which the sizes of the parts of the partitioning are given. In one the goal is to maximize the total edge weight within the same cluster. The other one also requires to locate a center within each cluster and the goal is to maximize the total distance from each vertex to its center. AMS subject classification: 05C70 Factorization, matching, covering and packing; 05C85 Graph algorithms. 1 Introduction Let G = (V; E) be a complete graph with vertex set V such that jV j = n, edge set E, and edge weights w(u; v) 0; (u; v) 2 E. A pmatching is a set of p disjoint edges in a graph. A pmatching with p = b n 2 c is called perf...
Simulated NBody: New Particle PhysicsBased Heuristics for a Euclidean LocationAllocation Problem
, 1999
"... The general facility location problem and its variants, including most locationallocation and Pmedian problems, are known to be NPhard combinatorial optimization problems. Consequently, there is now a substantial body of literature on heuristic algorithms for a variety of location problems, am ..."
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The general facility location problem and its variants, including most locationallocation and Pmedian problems, are known to be NPhard combinatorial optimization problems. Consequently, there is now a substantial body of literature on heuristic algorithms for a variety of location problems, among which can be found several versions of the wellknown simulated annealing algorithm. This paper presents an optimization paradigm that, like simulated annealing, is based on a particle physics analogy but is markedly different from simulated annealing. Two heuristics based on this paradigm are presented and compared to simulated annealing for a capacitated facility location problem on Euclidean graphs. Experimental results based on randomly generated graphs suggest that one of the heuristics outperforms simulated annealing both in cost minimization as well as execution time. The particular version of location problem considered here, a locationallocation problem, involves determi...
LP Rounding for kCenters with Nonuniform Hard Capacities
"... Abstract—In this paper we consider a generalization of the classical kcenter problem with capacities. Our goal is to select k centers in a graph, and assign each node to a nearby center, so that we respect the capacity constraints on centers. The objective is to minimize the maximum distance a node ..."
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Abstract—In this paper we consider a generalization of the classical kcenter problem with capacities. Our goal is to select k centers in a graph, and assign each node to a nearby center, so that we respect the capacity constraints on centers. The objective is to minimize the maximum distance a node has to travel to get to its assigned center. This problem is NPhard, even when centers have no capacity restrictions and optimal factor 2 approximation algorithms are known. With capacities, when all centers have identical capacities, a 6 approximation is known with no better lower bounds than for the infinite capacity version. While many generalizations and variations of this problem have been studied extensively, no progress was made on the capacitated version for a general capacity function. We develop the first constant factor approximation algorithm for this problem. Our algorithm uses an LP rounding approach to solve this problem, and works for the case of nonuniform hard capacities, when multiple copies of a node may not be chosen and can be extended to the case when there is a hard bound on the number of copies of a node that may be selected. Finally, for nonuniform soft capacities we present a much simpler 11approximation algorithm, which we find as one more evidence that hard capacities are much harder to deal with. Keywordsapproximation algorithms; kcenter; nonuniform capacities; hard capacities; LP rounding; I.
Exact and Approximation Algortihms for Clustering
, 1997
"... In this paper we present a n O(k1�1=d) time algorithm for solving the kcenter problem in R d, under L1 and L2 metrics. The algorithm extends to other metrics, and can be used to solve the discrete kcenter problem, as well. We also describe a simple (1 +)approximation algorithm for the kcenter pr ..."
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In this paper we present a n O(k1�1=d) time algorithm for solving the kcenter problem in R d, under L1 and L2 metrics. The algorithm extends to other metrics, and can be used to solve the discrete kcenter problem, as well. We also describe a simple (1 +)approximation algorithm for the kcenter problem, with running time O(n log k) + (k = ) O(k1�1=d). Finally, we present a n O(k1�1=d) time algorithm for solving the Lcapacitated kcenter problem, provided that L = (n=k 1�1=d) or L = O(1). We conclude with a simple approximation algorithm for the Lcapacitated kcenter problem.