14474506
Explicit OR-dispersers with polylogarithmic degree
An (<italic>N, M, T</italic>)-OR-disperser is a bipartite multigraph <italic>G</italic>=(<italic>V, W, E</italic>) with |<italic>V</italic>| = <italic>N</italic>, and |<italic>W</italic>| = <italic>M</italic>, having the following expansion property: any subset of <italic>V</italic> having at least <italic>T</italic> vertices has a neighbor set of size at least <italic>M</italic>/2. For any pair of constants &xgr;, λ, 1 ≥ &xgr; > λ ≥ 0, any sufficiently large <italic>N</italic>, and for any <italic>T</italic> ≥ 2<supscrpt>(log<italic>N</italic>)</supscrpt> <italic>M</italic> ≤ 2<supscrpt>(log <italic>N</italic>)<supscrpt>λ</supscrpt></supscrpt>, we give an explicit elementary construction of an (<italic>N, M,    T</italic>)-OR-disperser such that the out-degree of any vertex in <italic>V</italic> is at most polylogarithmic in <italic>N</italic>. Using this with known applications of OR-dispersers yields several results. First, our construction implies that the complexity class Strong-RP defined by Sipser, equals RP. Second, for any fixed &eegr; > 0, we give the first polynomial-time simulation of RP algorithms using the output of any “&eegr;-minimally random” source. For any integral <italic>R</italic> > 0, such a source accepts a single request for an <italic>R</italic>-bit string and generates the string according to a distribution that assigns probability at most 2<supscrpt>−R<supscrpt>&eegr;</supscrpt></supscrpt> to any string. It is minimally random in the sense that  any weaker source is insufficient to do a black-box polynomial-time simulation of RP algorithms.
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.
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.
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.
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.
12321308
Efficient gossip-based aggregate computation
Recently, there has been a growing interest in gossip-based protocols that employ randomized communication to ensure robust information dissemination. In this paper, we present a novel gossip-based scheme using which all the nodes in an n-node overlay network can compute the common aggregates of MIN, MAX, SUM, AVERAGE, and RANK of their values using O(n log log n) messages within O(log n log log n) rounds of communication. To the best of our knowledge, ours is the first result that shows how to compute these aggregates with high probability using only O(n log log n) messages. In contrast, the best known gossip-based algorithm for computing these aggregates requires O(nlog n) messages and O(log n) rounds. Thus, our algorithm allows system designers to trade off a small increase in round complexity with a significant reduction in message complexity. This can lead to dramatically lower network congestion and longer node lifetimes in wireless and sensor networks, where channel bandwidth and battery life are severely constrained.
5149437
The case for fair multiprocessor scheduling
In this paper, we compare the PD/sup 2/ Pfair algorithm to the EDF-FF partitioning scheme, which uses "first fit" (FF) as a partitioning heuristic and the earliest-deadline-first (EDF) algorithm for per-processor scheduling. We present experimental results that show that PD/sup 2/ is competitive with, and in some cases outperforms, EDF-FF. These results suggest that Pfair scheduling is a viable alternative to partitioning. Furthermore, as discussed herein, Pfair scheduling provides many additional benefits, such as simple and efficient synchronization, temporal isolation, fault tolerance, and support for dynamic tasks.
5519685
Efficient scheduling of soft real-time applications on multiprocessors
In this paper, we consider fair scheduling of soft real-time applications on multiprocessors using the earliest pseudo deadline first (EPDF) Pfair algorithm. Our main contributions are twofold. First, we establish a condition for ensuring a tardiness of at most one quantum under EPDF. This condition is very liberal and should often hold in practice. Second, we present simulation results involving randomly-generated task sets, including those that do not satisfy our condition. In these experiments, deadline misses were rare, and no misses by more than one quantum ever occurred.
16914350
Biochemical Knowledge Discovery Using Inductive Logic Programming
Machine Learning algorithms are being increasingly used for knowledge discovery tasks. Approaches can be broadly divided by distinguishing discovery of procedural from that of declarative knowledge. Client requirements determine which of these is appropriate. This paper discusses an experimental application of machine learning in an area related to drug design. The bottleneck here is in finding appropriate constraints to reduce the large number of candidate molecules to be synthesised and tested. Such constraints can be viewed as declarative specifications of the structuralel ements necessary for high medicinal activity and low toxicity. The first-order representation used within Inductive Logic Programming (ILP) provides an appropriate description language for such constraints. Within this application area knowledge accreditation requires not only a demonstration of predictive accuracy but also, and crucially, a certification of novel insight into the structuralc hemistry. This paper describes an experiment in which the ILP system Progolw as used to obtain structural constraints associated with mutagenicity of molecules. In doing so Progol found a new indicator of mutagenicity within a subset of previously published data. This subset was already known not to be amenable to statistical regression, though its complement was adequately explained by a linear model. According to the combined accuracy/explanation criterion provided in this paper, on both subsets comparative trials show that Progol's structurally-oriented hypotheses are preferable to those of other machine learning algorithms.