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.
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.
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.
7189804
Low-Bandwidth Routing and Electrical Power Networks
Given a graph G and a (multi-)set of pairs of vertices in it, the classical NP-hard maximum edge-disjoint-paths problem (MDP) is to connect as many of the given pairs as possible using pairwise edge-disjoint paths in G. We study a relative of this problem: we have a network with fixed link capacities that may have to service large demands when necessary. In particular, individual demands are allowed to exceed capacities, and thus flows for some request pairs necessarily have to be split into different flow-paths. This is the framework for computational problems arising from: (i) electrical power networks due to the proposed deregulation of the electric utility industry in the USA, and (ii) applications such as real-time Internet services (e.g., telephone, fax, video). We show that these problems come in a few variants, some efficiently solvable and many NP-hard; we also present approximation algorithms for many of the NP-hard variants presented. Some of our approximation algorithms benefit from certain improved tail estimates that we derive; the latter also yield improved approximations for a family of packing integer programs.
14399319
Improved distributed algorithms for coloring and network decomposition problems
This paper deals with the problems of computing a maximal independent set and a vertex coloring in a dktributed model of computation. Given a connected graph G = (V, E) with IVI = n and maximum degree A such that G is neither a complete graph nor an odd cycle, Brooks’ theorem shows that G can be colored with A colors. We generalize thk as follows: let G – w be A-colored; then, v can be colored by considering the vertices in an O(loga n) radius around v, and this is tight. Using this, we show that A-coloring G is reducible in 0(log3 n/log A) time to (A+ I)-vertex coloring G in a distributed model. This leads to fast distributed algorithms, and a linear–processor NC algorithm, for Acoloring. We also prove a tight Q(diameter(G)) lower bound for A-edge-coloring bipartite graphs, even with unlimited randomness. When A = 2, this implies an Q(n) lower bound for vertex coloring paths and even cycles. A fundamental notion in distributed graph algorithms is that of a cluster decomposition, introduced by Awerbuch, Goldberg, Luby and Plotkin. We improve the existing bounds by showing how to compute a cluster decomposition in O(n”(’(”)) ) time, where e(n) = 1/=. This implies improved bounds for several problems, such as computing a maximal independent set and a (A + I )-coloring. We also show how to compute a A–coloring within the same time bound, using our reduction technique. Next, we show that the problem of doing better than O(n”(’(m))) time for cluster decomposition is self-reducible to graphs of “intermediate” diameter and degree. This pinpoints the weak points of existing cluster decomposition algorithms. *This research was supported in part by NSF PYI award CGR89-96272 with matching support from UPS and Sun Microsystems. Permission to copy without fee ell or part of this material is granted provided that the copiss are not made or distributed for direct commercial advantage, the ACM copyright notica and tha title of the publication and its date appear, and notice ie given that copying is by permission of the Association for Computing Machinery. To copy otharwise, or to republish, requires a fee and/or specific permieaion. 24th ANNUAL ACM STOC 5/92/VICTORIA, B. C., CANADA a 1992 ACM 0-89791-51 2-7192 /000410!581 . ..$1.50
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.
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.
8870978
Monte Carlo Techniques for Estimating the Fiedler Vector in Graph Applications
Determiningthe Fiedler vector of the Laplacian or adjacency matrices of graphs is the most computationally intensive component of several applications, such as graph partitioning, graph coloring, envelope reduction, and seriation. Often an approximation of the Fiedler vector is sufficient.We discuss issues involved in the use of Monte Carlo techniques for this purpose.
9220714
Extracting Context-Sensitive Models in Inductive Logic Programming
Given domain-specific background knowledge and data in the form of examples, an Inductive Logic Programming (ILP) system extracts models in the data-analytic sense. We view the model-selection step facing an ILP system as a decision problem, the solution of which requires knowledge of the context in which the model is to be deployed. In this paper, "context" will be defined by the current specification of the prior class distribution and the client's preferences concerning errors of classification. Within this restricted setting, we consider the use of an ILP system in situations where: (a) contexts can change regularly. This can arise for example, from changes to class distributions or misclassification costs; and (b) the data are from observational studies. That is, they may not have been collected with any particular context in mind. Some repercussions of these are: (a) any one model may not be the optimal choice forall contexts; and (b) not all the background information provided may be relevant for all contexts. Using results from the analysis of Receiver Operating Characteristic curves, we investigate a technique that can equip an ILP system to reject those models that cannot possibly be optimal in any context. We present empirical results from using the technique to analyse two datasets concerned with the toxicity of chemicals (in particular, their mutagenic and carcinogenic properties). Clients can, and typically do, approach such datasets with quite different requirements. For example, a synthetic chemist would require models with a low rate of commission errors which could be used to direct efficiently the synthesis of new compounds. A toxicologist on the other hand, would prefer models with a low rate of omission errors. This would enable a more complete identification of toxic chemicals at a calculated cost of misidentification of non-toxic cases as toxic. The approach adopted here attempts to obtain a solution that contains models that are optimal for each such user according to the cost function that he or she wishes to apply. In doing so, it also provides one solution to the problem of how the relevance of background predicates is to be assessed in ILP.
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.
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.