44926291
Low Discrepancy Sets Yield Approximate Min-Wise Independent Permutation Families
Motivated by a problem of filtering near-duplicate Web documents, Broder, Charikar, Frieze & Mitzenmacher defined the following notion of e-approximate min-wise independent permutation families [2]. A multiset \(\mathcal{F}\) of permutations of {0,1, ... , n–1} is such a family if for all K ⊆ {0,1, ..., n–1} and any x ∈ K, a permutation π chosen uniformly at random form \(\mathcal{F}\) statisfies
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.
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.
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.
14773410
Algorithmic aspects of capacity in wireless networks
This paper considers two inter-related questions: (i) Given a wireless ad-hoc network and a collection of source-destination pairs {(si,ti)}, what is the maximum throughput capacity of the network, i.e. the rate at which data from the sources to their corresponding destinations can be transferred in the network? (ii) Can network protocols be designed that jointly route the packets and schedule transmissions at rates close to the maximum throughput capacity? Much of the earlier work focused on random instances and proved analytical lower and upper bounds on the maximum throughput capacity. Here, in contrast, we consider arbitrary wireless networks. Further, we study the algorithmic aspects of the above questions: the goal is to design provably good algorithms for arbitrary instances. We develop analytical performance evaluation models and distributed algorithms for routing and scheduling which incorporate fairness, energy and dilation (path-length) requirements and provide a unified framework for utilizing the network close to its maximum throughput capacity.Motivated by certain popular wireless protocols used in practice, we also explore "shortest-path like" path selection strategies which maximize the network throughput. The theoretical results naturally suggest an interesting class of congestion aware link metrics which can be directly plugged into several existing routing protocols such as AODV, DSR, etc. We complement the theoretical analysis with extensive simulations. The results indicate that routes obtained using our congestion aware link metrics consistently yield higher throughput than hop-count based shortest path metrics.
5246711
Dependent rounding in bipartite graphs
We combine the pipage rounding technique of Ageev & Sviridenko with a recent rounding method developed by Srinivasan (2001), to 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 the following applications: 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, and (iii) capacitated vertex cover; fair scheduling of jobs on unrelated parallel machines. A useful feature of our method is that it lets us prove certain (probabilistic) per-user fairness properties.
14860992
Scalable Time-Parallelization of Molecular Dynamics Simulations in Nano Mechanics
Molecular dynamics (MD) is an important atomistic simulation technique, with widespread use in computational chemistry, biology, and materials. An important limitation of MD is that the time step size is small, requiring a large number of iterations to simulate realistic time spans. Conventional parallelization is not very effective for this. We recently introduced a new approach to parallelization, where data from related prior simulations are used to parallelize a new computation along the time domain. In our prior work, the size of the physical system in the current simulation needed to be identical to that of the prior simulations. The significance of this paper lies in demonstrating a strategy that enables this approach to be used even when the physical systems differ in size. Furthermore, this method scaled up to almost 1000 processors with close to ideal speedup in one case, where conventional methods scale to only 2-3 processors
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.
18104124
A Note on Two Simple Transformations for Improving the Efficiency of an ILP System
Inductive Logic Programming (ILP) systems have had noteworthy successes in extracting comprehensible and accurate models for data drawn from a number of scientific and engineering domains. These results suggest that ILP methods could enhance the model-construction capabilities of software tools being developed for the emerging discipline of "knowledge discovery from databases." One significant concern in the use of ILP for this purpose is that of efficiency. The performance of modern ILP systems is principally affected by two issues: (1) they often have to search through very large numbers of possible rules (usually in the form of definite clauses); (2) they have to score each rule on the data (usually in the form of ground facts) to estimate "goodness". Stochastic and greedy approaches have been proposed to alleviate the complexity arising from each of these issues. While these techniques can result in order-of-magnitude improvements in the worst-case search complexity of an ILP system, they do so at the expense of exactness. As this may be unacceptable in some situations, we examine two methods that result in admissible transformations of clauses examined in a search. While the methods do not alter the size ofthe search space (that is, the number of clauses examined), they can alleviate the theorem-proving effort required to estimate goodness. The first transformation simply involves eliminating literals using a weak test for redundancy. The second involves partitioning the set of literals within a clause into groups that can be executed independently of each other. The efficacy ofthe se transformations are evaluated empirically on a number of well-known ILP datasets. The results suggest that for problems that require the use of highly nondeterminate predicates, the transformations can provide significant gains as the complexity of clauses sought increases.