1214 Nov. 2000
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Proceedings 41st Annual Symposium on Foundations of Computer Science
Publication Year: 2000 PDF (259 KB) 
Entropy waves, the zigzag graph product, and new constantdegree expanders and extractors
Publication Year: 2000, Page(s):3  13
Cited by: Papers (24)The main contribution is a new type of graph product, which we call the zigzag product. Taking a product of a large graph with a small graph, the resulting graph inherits (roughly) its size from the large one, its degree from the small one, and its expansion properties from both. Iteration yields simple explicit constructions of constantdegree expanders of every size, starting from one constant... View full abstract»

Universality and tolerance
Publication Year: 2000, Page(s):14  21
Cited by: Papers (5)For any positive integers r and n, let H(r,n) denote the family of graphs on n vertices with maximum degree r, and let H(r,n,n) denote the family of bipartite graphs H on 2n vertices with n vertices in each vertex class, and with maximum degree r. On one hand, we note that any H(r,n)universal graph must have /spl Omega/(n/sup 22/r/) edges. On the other hand, for any n/spl ges/n/sub 0/(r), we exp... View full abstract»

Extracting randomness via repeated condensing
Publication Year: 2000, Page(s):22  31
Cited by: Papers (15)On an input probability distribution with some (min)entropy an extractor outputs a distribution with a (near) maximum entropy rate (namely the uniform distribution). A natural weakening of this concept is a condenser, whose output distribution has a higher entropy rate than the input distribution (without losing much of the initial entropy). We construct efficient explicit condensers. The condens... View full abstract»

Extracting randomness from samplable distributions
Publication Year: 2000, Page(s):32  42
Cited by: Papers (51)The standard notion of a randomness extractor is a procedure which converts any weak source of randomness into an almost uniform distribution. The conversion necessarily uses a small amount of pure randomness, which can be eliminated by complete enumeration in some, but not all, applications. We consider the problem of deterministically converting a weak source of randomness into an almost uniform... View full abstract»

Pseudorandom generators in propositional proof complexity
Publication Year: 2000, Page(s):43  53
Cited by: Papers (13)We call a pseudorandom generator G/sub n/:{0,1}/sup n//spl rarr/{0,1}/sup m/ hard for a propositional proof system P if P can not efficiently prove the (properly encoded) statement G/sub n/(x/sub 1/,...,x/sub n/)/spl ne/b for any string b/spl epsiv/{0,1}/sup m/. We consider a variety of "combinatorial" pseudorandom generators inspired by the NisanWigderson generator on one hand, and by the constr... View full abstract»

Stochastic models for the Web graph
Publication Year: 2000, Page(s):57  65
Cited by: Papers (114)  Patents (24)The Web may be viewed as a directed graph each of whose vertices is a static HTML Web page, and each of whose edges corresponds to a hyperlink from one Web page to another. We propose and analyze random graph models inspired by a series of empirical observations on the Web. Our graph models differ from the traditional G/sub n,p/ models in two ways: 1. Independently chosen edges do not result in th... View full abstract»

Optimization problems in congestion control
Publication Year: 2000, Page(s):66  74
Cited by: Papers (16)One of the crucial elements in the Internet's success is its ability to adequately control congestion. The paper defines and solves several optimization problems related to Internet congestion control, as a step toward understanding the virtues of the TCP congestion control algorithm currently used and comparing it with alternative algorithms. We focus on regulating the rate of a single unicast fl... View full abstract»

Fairness measures for resource allocation
Publication Year: 2000, Page(s):75  85
Cited by: Papers (19)  Patents (1)In many optimization problems, one seeks to allocate a limited set of resources to a set of individuals with demands. Thus, such allocations can naturally be viewed as vectors, with one coordinate representing each individual. Motivated by work in network routing and bandwidth assignment, we consider the problem of producing solutions that simultaneously approximate all feasible allocations in a c... View full abstract»

On the approximability of tradeoffs and optimal access of Web sources
Publication Year: 2000, Page(s):86  92
Cited by: Papers (80)We study problems in multiobjective optimization, in which solutions to a combinatorial optimization problem are evaluated with respect to several cost criteria, and we are interested in the tradeoff between these objectives (the socalled Pareto curve). We point out that, under very general conditions, there is a polynomially succinct curve that /spl epsiv/approximates the Pareto curve, for any... View full abstract»

How bad is selfish routing?
Publication Year: 2000, Page(s):93  102
Cited by: Papers (63)We consider the problem of routing traffic to optimize the performance of a congested network. We are given a network, a rate of traffic between each pair of nodes, and a latency function for each edge specifying the time needed to traverse the edge given its congestion; the objective is to route traffic such that the sum of all travel timesthe total latencyis minimized. In many settings, includ... View full abstract»

A polylogarithmic approximation of the minimum bisection
Publication Year: 2000, Page(s):105  115
Cited by: Papers (11)  Patents (1)A bisection of a graph with n vertices is a partition of its vertices into two sets, each of size n/2. The bisection cost is the number of edges connecting the two sets. Finding the bisection of minimum cost is NPhard. We present an algorithm that finds a bisection whose cost is within ratio of O(log/sup 2/ n) from the optimal. For graphs excluding any fixed graph as a minor (e.g. planar graphs) ... View full abstract»

Approximability and inapproximability results for nowait shop scheduling
Publication Year: 2000, Page(s):116  125
Cited by: Papers (1)We investigate the approximability of nowait shop scheduling problems under the makespan criterion. In a flow shop, all jobs pass through the machines in the same ordering. In the more general job shop, the routes of the jobs are jobdependent. We present a polynomial time approximation scheme (PTAS) for the nowait flow shop problem on any fixed number of machines. Unless P=NP, this result canno... View full abstract»

Nested graph dissection and approximation algorithms
Publication Year: 2000, Page(s):126  135This paper considers approximation algorithms for graph completion problems using the nested dissection paradigm. Given a superadditive function of interest (the smallest planar or chordal extension for example) and a test that relates it to an upper bound of the smallest separator, we provide a framework how to dissect the graph recursively such that no subgraph has more than half the value of i... View full abstract»

Approximating the single source unsplittable mincost flow problem
Publication Year: 2000, Page(s):136  145
Cited by: Papers (4)In the single source unsplittable mincost flow problem, commodities must be routed simultaneously from a common source vertex to certain destination vertices in a given graph with edge capacities and costs; the demand of each commodity must be routed along a single path and the total cost must not exceed a given budget. This problem has been introduced by J.M. Kleinberg (1996) and generalizes sev... View full abstract»

Hardness of approximate hypergraph coloring
Publication Year: 2000, Page(s):149  158
Cited by: Papers (10)We introduce the notion of covering complexity of a probabilistic verifier. The covering complexity of a verifier on a given input is the minimum number of proofs needed to "satisfy" the verifier on every random string, i.e., on every random string, at least one of the given proofs must be accepted by the verifier. The covering complexity of PCP verifiers offers a promising route to getting strong... View full abstract»

"Softdecision" decoding of Chinese remainder codes
Publication Year: 2000, Page(s):159  168
Cited by: Papers (21)  Patents (1)Given n relatively prime integers p/sub 1/<...<p/sub n/ and an integer k<n, the Chinese Remainder Code, CRT/sub p1,...,pnik/, has as its message space M={0,...,/spl Pi//sub i=1//sup k/,pi1}, and encodes a message m /spl isin/M as the vector <m/sub 1/,...,m/sub n/>, where m/sub i/=m(mod p/sub i/). The softdecision decoding problem for the Chinese remainder code is given as input a ... View full abstract»

Superlinear timespace tradeoff lower bounds for randomized computation
Publication Year: 2000, Page(s):169  179
Cited by: Papers (9)We prove the first timespace lower bound tradeoffs for randomized computation of decision problems. The bounds hold even in the case that the computation is allowed to have arbitrary probability of error on a small fraction of inputs. Our techniques are an extension of those used by M. Ajtai (1999) in his timespace tradeoffs for deterministic RAM algorithms computing element distinctness and for... View full abstract»

On the hardness of graph isomorphism
Publication Year: 2000, Page(s):180  186
Cited by: Papers (5)We show that the graph isomorphism problem is hard under logarithmic space manyone reductions for the complexity classes NL, PL (probabilistic logarithmic space), for every logarithmic space modular class Mod/sub k/L and for the class DET of problems NC/sup 1/ reducible to the determinant. These are the strongest existing hardness results for the graph isomorphism problem, and imply a randomized ... View full abstract»

Stable distributions, pseudorandom generators, embeddings and data stream computation
Publication Year: 2000, Page(s):189  197
Cited by: Papers (48)  Patents (20)In this paper we show several results obtained by combining the use of stable distributions with pseudorandom generators for bounded space. In particular: we show how to maintain (using only O(log n//spl epsiv//sup 2/) words of storage) a sketch C(p) of a point p/spl isin/l/sub 1//sup n/ under dynamic updates of its coordinates, such that given sketches C(p) and C(q) one can estimate pq/sub 1/ ... View full abstract»

New data structures for orthogonal range searching
Publication Year: 2000, Page(s):198  207
Cited by: Papers (32)We present new general techniques for static orthogonal range searching problems in two and higher dimensions. For the general range reporting problem in R/sup 3/, we achieve query time O(log n+k) using space O(n log/sup 1+/spl epsiv// n), where n denotes the number of stored points and k the number of points to be reported. For the range reporting problem on an n/spl times/n grid, we achieve quer... View full abstract»

Nearly optimal expectedcase planar point location
Publication Year: 2000, Page(s):208  218
Cited by: Papers (2)We consider the planar point location problem from the perspective of expected search time. We are given a planar polygonal subdivision S and for each polygon of the subdivision the probability that a query point lies within this polygon. The goal is to compute a search structure to determine which cell of the subdivision contains a given query point, so as to minimize the expected search time. Th... View full abstract»

On levels in arrangements of curves
Publication Year: 2000, Page(s):219  227
Cited by: Papers (1)Analyzing the worstcase complexity of the klevel in a planar arrangement of n curves is a fundamental problem in combinatorial geometry. We give the first subquadratic upper bound (roughly O(nk/sup 12/3/*)) for curves that are graphs of polynomial functions of an arbitrary fixed degree s. Previously, nontrivial results were known only for the case s=1 and s=2. We also improve the earlier bound ... View full abstract»

Detecting a network failure
Publication Year: 2000, Page(s):231  239
Cited by: Papers (9)Measuring the properties of a large, unstructured network can be difficult: one may not have full knowledge of the network topology, and detailed global measurements may be infeasible. A valuable approach to such problems is to take measurements from selected locations within the network and then aggregate them to infer largescale properties. One sees this notion applied in settings that range fr... View full abstract»

Testing of clustering
Publication Year: 2000, Page(s):240  250
Cited by: Papers (5)A set X of points in /spl Rfr//sup d/ is (k,b)clusterable if X can be partitioned into k subsets (clusters) so that the diameter (alternatively, the radius) of each cluster is at most b. We present algorithms that by sampling from a set X, distinguish between the case that X is (k,b)clusterable and the case that X is /spl epsiv/far from being (k,b')clusterable for any given 0</spl epsiv//sp... View full abstract»