17073164
Improved approximations of packing and covering problems
Aravind Srinivasant Several important NP-hard combinatorial optimization problems can be posed as packing\couerirag integer pragramq the rarzrfomized rouradingtechnique of Raghavan & Thompson is a powerful tool to approximate them well. We present one elementary unifying property of all these integer programs (IPs), and use the FKG correlation inequality to derive an improved analysis of randomized rounding on them. Thk also yields a pessimistic estimator, thus presenting deter-ministic polynomial-time algorithms for them with approximation guarantees significantly better than those known.
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.
2380498
Improved bounds and algorithms for hypergraph two-coloring
We show that for all large n, every n-uniform hypergraph with at most 0.7/spl radic/(n/lnn)/spl times/2/sup n/ edges can be two-colored. We, in fact, present fast algorithms that output a proper two-coloring with high probability for such hypergraphs. We also derandomize and parallelize these algorithms, to derive NC/sup 1/ versions of these results. This makes progress on a problem of Erdos (1963), improving the previous-best bound of n/sup 1/3-0(1)//spl times/2/sup n/ due to Beck (1978). We further generalize this to a "local" version, improving on one of the first applications of the Lovasz Local Lemma.
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
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.
2418753
Computing with very weak random sources
For any fixed /spl epsiv/>0, we show how to simulate RP algorithms in time n/sup O(log n/) using the output of a /spl delta/-source with min-entropy R(/spl epsiv/). Such a weak random source is asked once for R(/spl epsiv/) bits; it outputs an R-bit string such that any string has probability at most 2/sup -R/(/spl epsiv//). If /spl epsiv/>1-1/(k+1), our BPP simulations take time n/sup O(log(k/ n)) (log/sup (k/) is the logarithm iterated k times). We also give a polynomial-time BPP simulation using Chor-Goldreich sources of min-entropy R/sup /spl Omega/(1/), which is optimal. We present applications to time-space tradeoffs, expander constructions, and the hardness of approximation. Also of interest is our randomness-efficient Leftover Hash Lemma, found independently by Goldreich and Wigderson.<<ETX>>
16380223
Learning Chomsky-like Grammars for Biological Sequence Families
This paper presents a new method of measuring performance when positives are rare and investigates whether Chomsky-like grammar representations are useful for learning accurate comprehensible predictors of members of biological sequence families. The positive-only learning framework of the Inductive Logic Programming (ILP) system CProgol is used to generate a grammar for recognising a class of proteins known as human neuropeptide precursors (NPPs). As far as these authors are aware, this is both the first biological grammar learnt using ILP and the first real-world scientific application of the positive-only learning framework of CProgol. Performance is measured using both predictive accuracy and a new cost function, em Relative Advantage (RA). The RA results show that searching for NPPs by using our best NPP predictor as a filter is more than 100 times more efficient than randomly selecting proteins for synthesis and testing them for biological activity. The highest RA was achieved by a model which includes grammar-derived features. This RA is significantly higher than the best RA achieved without the use of the grammar-derived features.
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.
11919636
Quick-release fair scheduling
In prior work on multiprocessor fairness, efficient techniques with provable properties for reallocating spare processing capacity have been elusive. In this paper, we address this shortcoming by proposing a new notion of multiprocessor fairness, called quick-release fair (QRfair) scheduling. Under QRfair scheduling, each task is specified by giving both a minimum and a maximum weight (i.e., processor share). The goal is to schedule each task (as the spare capacity changes) at a rate that is (i) at least that implied by its minimum weight and (ii) at most that implied by its maximum weight. We present a quick-release variant of the PD/sup 2/ Pfair scheduling algorithm called PD/sup Q/ and prove that the allocations of PD/sup Q/ always satisfy (i) and (ii). Also, we present results from simulation experiments that show the efficacy of PD/sup Q/.
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.
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.