15901085
Improved Approximation Guarantees for Packing and Covering Integer Programs
Several important NP-hard combinatorial optimization problems can be posed as packing/covering integer programs; the randomized rounding technique of Raghavan and Thompson is a powerful tool with which to approximate them well. We present one elementary unifying property of all these integer linear programs and use the FKG correlation inequality to derive an improved analysis of randomized rounding on them. This yields a pessimistic estimator, thus presenting deterministic polynomial-time algorithms for them with approximation guarantees that are significantly better than those known.
23028632
Mechanism design for intellectual property rights protection
Estimates for the annual size of software piracy are in the region of $15 billion. The problem is also manifest in other forms of intellectual property. The explosive growth of the Internet and other communications networks has accentuated this problem. The new infrastructure has facilitated piracy by effectively reducing the cost of copying to negligible levels. (Recently, the FBI launched an operation called “Cyber Strike,” with the objective of curbing illegal copying and distribution of software over computer networks.) A naive suggestion has been that intellectual property rights (IPR) violation is actually beneficial from the social point of view, since it decreases the monopoly power of the provider. However, the flip side of this argument is that the IPR violations decrease the incentive for innovation because they lead to lower profits. In this paper, several mechanisms for IPR protection are designed. The mechanisms involve two tools: the level of enforcement (i.e., the probability that an IPR violator will be apprehended) and the penalty to be levied on an apprehended IPR violator. These tools are analyzed by considering the tradeoff between social welfare and the provider’s profit. The paper considers a provider who wants to maximize his profit and a policy maker who wants to maximize “net” social welfare (defined as welfare less any costs of enforcement), subject to a target profit for the provider. The consumers choose from among three options: buy, copy, or stay out of the market. A game-theoretic framework is adopted, where the policy maker, the provider, and the consumers get to move in that order. Among the results, the research shows that
8959226
Low-Discrepancy Sets For High-Dimensional Rectangles: A Survey
A sub-area of discrepancy theory that has received much attention in computer science recently, is that of explicit constructions of low-discrepancy point sets for various types of rectangle families in high dimension. This research has led to interesting applications in error-control coding, distributed protocols, Web document filtering, derandomization, and other areas. We give a short survey of this area here.
8868988
Contention resolution with constant expected delay
We study contention resolution in a multiple-access channel such as the Ethernet channel. In the model that we consider, n users generate messages for the channel according to a probability distribution. Raghavan and Upfal have given a protocol in which the expected delay (time to get serviced) of every message is O(log n) when messages are generated according to a Bernoulli distribution with generation rate up to about 1/10. Our main results are the following protocols: (a) one in which the expected average message delay is O(1) when messages are generated according to a Bernoulli distribution with a generation rate smaller than 1/e, and (b) one in which the expected delay of any message is O(1) for an analogous model in which users are synchronized (i.e., they agree about the time), there are potentially an infinite number of users, and messages are generated according to a Poisson distribution with generation rate up to 1/e. (Each message constitutes a new user.)
To achieve (a), we first show how to simulate (b) using n synchronized users, and then show how to build the synchronization into the protocol.
39527744
Efficient Algorithms for the Minimum Weighted Dominating Clique Problem on Permutation Graphs
Given a graph G=(V, E) with real weights assigned to its vertices, a clique of G that also dominates its vertex set V, is called a dominating clique (DC) of G. Given a permutation graph G with all its vertices having nonnegative weights, and its permutation representation, the problem addressed in this paper is that of finding any minimum weight DC of G. We improve the existing O(|V|2) algorithm for this problem to O(|V|log|V|). The space complexity of our algorithm is O(|V|). We also present a |V| processor, O(log|V|) time, O(|V|log|V|) space parallel EREW PRAM algorithm for this problem.
12370019
New algorithmic aspects of the Local Lemma with applications to routing and partitioning
The Lovasz local lemma (LLL)is a powerful tool that is increasingly playing a valuable role in computer science. The original lemma was nonconstructive; a breakthrough of Beck and its generalizations (due to Alon and Molloy and Reed)have led to constructive versions. However, these methods do not capture some classes of applications of the LLL. We make progress on this by providing algorithmic approaches to two families of applications of the LLL. The first provides constructive versions of certain applications of an extension of the LLL (modeling, e.g., hypergraph-partitioning and low-congestion routing problems); the second provides new algorithmic results on constructing disjoint paths in graphs. Our results can also be seen as constructive upper bounds on the integrality gap of certain packing problems. One common theme of our work is a "gradual rounding" approach.
6168494
Approximation algorithms for scheduling on multiple machines
We develop a single rounding algorithm for scheduling on unrelated parallel machines; this algorithm works well with the known linear programming, quadratic programming, and convex programming-relaxations for scheduling to minimize completion time, makespan, and other well-studied objective functions. We obtain the following applications for the general setting of unrelated parallel machines: (i) a bicriteria algorithm for a schedule whose weighted completion-time and makespan simultaneously exhibit the current-best individual approximations for these criteria (3/2 and 2, respectively); (ii) better-than-two approximation guarantees for scheduling under the L/sub p/ norm for all 1 < p < /spl infin/, improving on the 2-approximation algorithms of Azar & Epstein; and (iii) the first constant-factor multicriteria approximation algorithms that handle the weighted completion-time and any given collection of integer L/sub p/ norms. Our algorithm yields a common generalization of rounding theorems due to Karp et al and Shmoys & Tardos; among other applications, this yields an improved approximation for scheduling with resource-dependent processing times studied by Grigoriev et al.
9141341
Dependent rounding and its applications to approximation algorithms
We develop a new randomized rounding approach for fractional vectors defined on the edge-sets of bipartite graphs. We show various ways of combining this technique with other ideas, leading to improved (approximation) algorithms for various problems. These include:---low congestion multi-path routing;---richer random-graph models for graphs with a given degree-sequence;---improved approximation algorithms for: (i) throughput-maximization in broadcast scheduling, (ii) delay-minimization in broadcast scheduling, as well as (iii) capacitated vertex cover; and---fair scheduling of jobs on unrelated parallel machines.
36878064
A Compact Storage Scheme for Fast Wavelet-Based Subregion Retrieval
In an image browsing environment there is need for progressively viewing image subregions at various resolutions. We describe a storage scheme that accomplishes good image compression, while supporting fast image subregion retrieval. We evaluate analytically and experimentally the compression performance of our algorithm. We also provide results on the speed of the algorithm to demonstrate its effectiveness, and present an extension to a client/server environment.
11533466
Edge Domination on Bipartite Permutation Graphs and Cotriangulated Graphs
An edge dominating set D of graph G = (V, E) is a set of edges such that every edge not in D is adjacent to at least one edge in D. We develop polynomial time algorithms for finding a minimum edge dominating set for a cotriangulated graph and a bipartite permutation graph.
36642411
Parameterizing parallel multiplicative lagged-Fibonacci generators
Monte Carlo computations are commonly considered to be naturally parallel. However, one needs to exercise care in parallelizing the underlying pseudorandom number generator (PRNG) to avoid correlations within, and between, random number streams. PRNGs are normally parallelized using one of the following two paradigms: (i) cycle division and (ii) parameterization. Most of the popular PRNGs based on linear recurrences, such as linear congruential generators (LCGs), generalized feedback shift-register generators (GFSRs), and additive lagged-Fibonacci generators (ALFGs) have been parallelized using both these paradigms. While the (nonlinear) multiplicative lagged-Fibonacci generators (MLFG) is considered superior to the ALFG in quality, it had so far been parallelized only via the cycle division paradigm, which has its limitations. In this paper, we describe parallelization of the MLFG using parameterization, and discuss its implementation in the Scalable Parallel Random Number Generators (SPRNG) [ACM Trans. Math. Software 26 (2000) 436] parallel pseudorandom number generation software. We also present empirical results demonstrating the quality, and quantitatively compare the parallel ALFGs and MLFGs quality.