Proceedings of 37th Conference on Foundations of Computer Science
Latest Published Articles

Load balancing and density dependent jump Markov processes
Tue Aug 06 00:00:00 EDT 2002 Tue Aug 06 00:00:00 EDT 2002 
Equivalence in finitevariable logics is complete for polynomial time
Tue Aug 06 00:00:00 EDT 2002 Tue Aug 06 00:00:00 EDT 2002 
Gadgets, approximation, and linear programming
Tue Aug 06 00:00:00 EDT 2002 Tue Aug 06 00:00:00 EDT 2002 
Sampling according to the multivariate normal density
Tue Aug 06 00:00:00 EDT 2002 Tue Aug 06 00:00:00 EDT 2002 
Path coloring on the mesh
Tue Aug 06 00:00:00 EDT 2002 Tue Aug 06 00:00:00 EDT 2002
Popular Articles

Polynomial time approximation schemes for Euclidean TSP and other geometric problems
Tue Aug 06 00:00:00 EDT 2002 Tue Aug 06 00:00:00 EDT 2002 
Probabilistic approximation of metric spaces and its algorithmic applications
Tue Aug 06 00:00:00 EDT 2002 Tue Aug 06 00:00:00 EDT 2002 
Spectral partitioning works: planar graphs and finite element meshes
Tue Aug 06 00:00:00 EDT 2002 Tue Aug 06 00:00:00 EDT 2002 
Faulttolerant quantum computation
Tue Aug 06 00:00:00 EDT 2002 Tue Aug 06 00:00:00 EDT 2002 
A polynomialtime algorithm for learning noisy linear threshold functions
Tue Aug 06 00:00:00 EDT 2002 Tue Aug 06 00:00:00 EDT 2002
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Polynomial time approximation schemes for Euclidean TSP and other geometric problems
Publication Year: 1996, Page(s):2  11
Cited by: Papers (44)We present a polynomial time approximation scheme for Euclidean TSP in ℜ^{2}. Given any n nodes in the plane and ε>0, the scheme finds a (1+ε)approximation to the optimum traveling salesman tour in time n^{0(1/ε)}. When the nodes are in ℜ^{d}, the running time increases to n(O˜(log^{d2}n)/ε^{d1}) The previous best appr... View full abstract»

Probabilistic approximation of metric spaces and its algorithmic applications
Publication Year: 1996, Page(s):184  193
Cited by: Papers (94)  Patents (9)This paper provides a novel technique for the analysis of randomized algorithms for optimization problems on metric spaces, by relating the randomized performance ratio for any, metric space to the randomized performance ratio for a set of “simple” metric spaces. We define a notion of a set of metric spaces that probabilisticallyapproximates another metric space. We prove that any met... View full abstract»

Spectral partitioning works: planar graphs and finite element meshes
Publication Year: 1996, Page(s):96  105
Cited by: Papers (27)  Patents (1)Spectral partitioning methods use the Fiedler vectorthe eigenvector of the secondsmallest eigenvalue of the Laplacian matrixto find a small separator of a graph. These methods are important components of many scientific numerical algorithms and have been demonstrated by experiment to work extremely well. In this paper, we show that spectral partitioning methods work well on boundeddegree plana... View full abstract»

Faulttolerant quantum computation
Publication Year: 1996, Page(s):56  65
Cited by: Papers (42)  Patents (6)It has recently been realized that use of the properties of quantum mechanics might speed up certain computations dramatically. Interest in quantum computation has since been growing. One of the main difficulties in realizing quantum computation is that decoherence tends to destroy the information in a superposition of states in a quantum computer making long computations impossible. A further dif... View full abstract»

A polynomialtime algorithm for learning noisy linear threshold functions
Publication Year: 1996, Page(s):330  338
Cited by: Papers (8)The authors consider the problem of learning a linear threshold function (a halfspace in n dimensions, also called a “perceptron”). Methods for solving this problem generally fall into two categories. In the absence of noise, this problem can be formulated as a linear program and solved in polynomial time with the ellipsoid algorithm (or interior point methods). On the other hand, simp... View full abstract»

Polynomial simulations of decohered quantum computers
Publication Year: 1996, Page(s):46  55
Cited by: Papers (5)Recently it has become clear, that a key issue in quantum computation is understanding how interaction with the environment, or “decoherence”, affects the computational power of quantum computers. We adopt the standard physical method of describing systems which are interwound with their environment by “density matrices”, and within this framework define a model of decohere... View full abstract»

Gadgets, approximation, and linear programming
Publication Year: 1996, Page(s):617  626
Cited by: Papers (8)The authors present a linearprogramming based method for finding “gadgets”, i.e., combinatorial structures reducing constraints of one optimization problem to constraints of another. A key step in this method is a simple observation which limits the search space to a finite one. Using this new method they present a number of new, computerconstructed gadgets for several different redu... View full abstract»

The Boolean isomorphism problem
Publication Year: 1996, Page(s):422  430
Cited by: Papers (5)  Patents (1)We investigate the computational complexity of the Boolean isomorphism problem (BI): on input of two Boolean formulas F and G decide whether there exists a permutation of the variables of G such that F and G become equivalent. Our main result is a oneround interactive proof for BI, where the verifier has access to an NP oracle. To obtain this, we use a recent result from learning theory by N. Bsh... View full abstract»

Fast faulttolerant concurrent access to shared objects
Publication Year: 1996, Page(s):570  579
Cited by: Papers (7)  Patents (41)The authors consider a synchronous model of distributed computation in which n nodes communicate via pointtopoint messages, subject to the following constraints: (i) in a single “step”, a node can only send or receive O(logn) words, and (ii) communication is unreliable in that a constant fraction of all messages are lost at each step due to node and/or link failures. They design and ... View full abstract»

Approximating minimumsize kconnected spanning subgraphs via matching
Publication Year: 1996, Page(s):292  301
Cited by: Papers (4)An efficient heuristic is presented for the problem of finding a minimumsize kconnected spanning subgraph of a given (undirected or directed) graph G=(V,E). There are four versions of the problem, depending on whether G is undirected or directed, and whether the spanning subgraph is required to be knode connected (kNCSS) or kedge connected (kECSS). The approximation guarantees are as follows... View full abstract»

Singlesource unsplittable flow
Publication Year: 1996, Page(s):68  77
Cited by: Papers (33)The maxflow mincut theorem of Ford and Fulkerson is based on an even more foundational result, namely Menger's theorem on graph connectivity Menger's theorem provides a good characterization for the following singlesource disjoint paths problem: given a graph G, with a source vertex s and terminals t_{1},...,t_{k}, decide whether there exist edgedisjoint st_{i} paths f... View full abstract»

Computationally hard algebraic problems
Publication Year: 1996, Page(s):284  289In this paper we present a simple geometriclike series of elements in a finite field F_{q}, and show that computing its sum is NPhard. This problem is then reduced to the problem of counting mod p the number of zeroes in a linear recurrence sequence with elements in a finite F_{p}, where p is a small prime. Hence the latter problem is also NPhard. In the lecture we shall also su... View full abstract»

Sampling according to the multivariate normal density
Publication Year: 1996, Page(s):204  212
Cited by: Papers (1)This paper deals with the normal density of n dependent random variables. This is a function of the form: ce(x^{T}Ax) where A is an n×n positive definite matrix, a: is the nvector of the random variables and c is a suitable constant. The first problem we consider is the (approximate) evaluation of the integral of this function over the positive orthant ∫(x_{1}=0)... View full abstract»

An 8approximation algorithm for the subset feedback vertex set problem
Publication Year: 1996, Page(s):310  319
Cited by: Papers (2)We present an 8approximation algorithm for the problem of finding a minimum weight subset feedback vertex set. The input in this problem consists of an undirected graph G=(V,E) with vertex weights w(v) and a subset of vertices S called special vertices. A cycle is called interesting if it contains at least one special vertex. A subset of vertices is called a subset feedback vertex set with respec... View full abstract»

The regularity lemma and approximation schemes for dense problems
Publication Year: 1996, Page(s):12  20
Cited by: Papers (20)There are two main contributions of the present paper. In the first, we use the constructive version of the Regularity Lemma to give directly simple polynomial time approximation schemes for several graph “subdivision” problems in dense graphs including the Max Cut problem, the Graph Bisection problem, the Min lway cut problem and Graph Separator problem. Arora, Karger and Karpinski (... View full abstract»

Binary space partitions for fat rectangles
Publication Year: 1996, Page(s):482  491The authors consider the practical problem of constructing binary space partitions (BSPs) for a set S of n orthogonal, nonintersecting, twodimensional rectangles in
R ^{3} such that the aspect ratio of each rectangle in S is at most α, for some constant a α⩾1. They present an n2^{O(√logn)}time algorithm to build a binary space partition of size n2... View full abstract» 
Load balancing and density dependent jump Markov processes
Publication Year: 1996, Page(s):213  222
Cited by: Papers (16)  Patents (1)We provide a new approach for analyzing both static and dynamic randomized load balancing strategies. We demonstrate the approach by providing the first analysis of the following model: customers arrive as a Poisson stream of rate λ_{n}, λ<1, at a collection of n servers. Each customer chooses some constant d servers independently and uniformly at random from the n servers... View full abstract»

A new rounding procedure for the assignment problem with applications to dense graph arrangement problems
Publication Year: 1996, Page(s):21  30
Cited by: Papers (9)We present a randomized procedure for rounding fractional perfect matchings to (integral) matchings. If the original fractional matching satisfies any linear inequality, then with high probability, the new matching satisfies that linear inequality in an approximate sense. This extends the wellknown LP rounding procedure of Raghavan and Thompson (1987), which is usually used to round fractional so... View full abstract»

Median selection requires (2+ϵ)n comparisons
Publication Year: 1996, Page(s):125  134
Cited by: Papers (1)Improving a long standing result of Bent and John (1985), we obtain a (2+ε)n lower bound (for some fixed ε>0) on the number of comparisons required, in the worst case, for selecting the median of n elements. The new lower bound is obtained using a weight function that allows us to combine leaf counting and adversary arguments View full abstract»

Factoring graphs to bound mixing rates
Publication Year: 1996, Page(s):194  203
Cited by: Papers (2)This paper develops a new technique for bounding the mixing rate of a Markov chain by decomposing the state space into factors. The first application is an efficient Monte Carlo Markov chain algorithm for generating random threecolorings of 2dimensional lattice regions. This provides a rigorous tool for studying some properties of the 3state Potts model and the ice model from statistical mechan... View full abstract»

Computing permanents over fields of characteristic 3: where and why it becomes difficult
Publication Year: 1996, Page(s):108  114
Cited by: Papers (1)In this paper we consider the complexity of computing permanents over fields of characteristic 3. We present a polynomial time algorithm for computing per(A) for a matrix A such that the rank rg(AA^{T}I)⩽1. On the other hand, we show that existence of a polynomialtime algorithm for computing per(A) for a matrix A such that rg(AA^{T}I)⩾2 implies NP=R. As a byproduct we ob... View full abstract»

Highly faulttolerant parallel computation
Publication Year: 1996, Page(s):154  163
Cited by: Papers (26)We reintroduce the coded model of faulttolerant computation in which the input and output of a computational device are treated as words in an errorcorrecting code. A computational device correctly computes a function in the coded model if its input and output, once decoded, are a valid input and output of the function. In the coded model, it is reasonable to hope to simulate all computational ... View full abstract»

Efficient approximate and dynamic matching of patterns using a labeling paradigm
Publication Year: 1996, Page(s):320  328
Cited by: Papers (12)  Patents (6)A key approach in string processing algorithmics has been the labeling paradigm which is based on assigning labels to some of the substrings of a given string. If these labels are chosen consistently, they can enable fast comparisons of substrings. Until the first optimal parallel algorithm for suffix tree construction was given by the authors in 1994 the labeling paradigm was considered not to be... View full abstract»

Tree data structures for Nbody simulation
Publication Year: 1996, Page(s):224  233
Cited by: Papers (2)In this paper, we study data structures for use in Nbody simulation. We concentrate on the spatial decomposition tree used in particlecluster force evaluation algorithms such as the BarnesHut algorithm. We prove that a kd tree is asymptotically inferior to a spatially balanced tree. We show that the worst case complexity of the force evaluation algorithm using a kd tree is Θ(nlog^{3<... View full abstract»}

New algorithms for the disk scheduling problem
Publication Year: 1996, Page(s):550  559
Cited by: Papers (10)  Patents (2)Processor speed and memory capacity are increasing several times faster than disk speed. This disparity suggests that disk I/O performance will become an important bottleneck. Methods are needed for using disks more efficiently. Past analysis of disk scheduling algorithms has largely been experimental and little attempt has been made to develop algorithms with provable performance guarantees. We c... View full abstract»

Efficient selftesting/selfcorrection of linear recurrences
Publication Year: 1996, Page(s):602  611
Cited by: Papers (1)The authors consider the problem of designing selftesters/selfcorrectors for functions defined by linear recurrences. They present the first complete package of efficient and simple selftesters, selfcorrectors, and resultcheckers for such functions. The results are proved by demonstrating an efficient reduction from this problem to the problem of testing linear functions over certain matrix g... View full abstract»

Property testing and its connection to learning and approximation
Publication Year: 1996, Page(s):339  348
Cited by: Papers (13)The authors study the question of determining whether an unknown function has a particular property or is εfar from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query the function on instances of its choice. First, they establish some connections between propert... View full abstract»

Equivalence in finitevariable logics is complete for polynomial time
Publication Year: 1996, Page(s):264  273
Cited by: Papers (2)How difficult is it to decide whether two finite structures can be distinguished in a given logic? For first order logic, this question is equivalent to the graph isomorphism problem with its wellknown complexity theoretic difficulties. Somewhat surprisingly, the situation is much clearer when considering the fragments L^{k} of firstorder logic whose formulae contain at most k (free or b... View full abstract»

Universal data compression and portfolio selection
Publication Year: 1996, Page(s):534  538
Cited by: Papers (5)  Patents (1)The authors consider universal data compression, universal portfolio selection (online portfolio algorithms) and the relationship of both to information theory. Apparently the fundamental minimax redundancy game in data compression and the minimax regret game for the growth rate of wealth in investment have the same answer. There is also a duality between entropy rate and the growth rate of wealth View full abstract»

Discrepancy sets and pseudorandom generators for combinatorial rectangles
Publication Year: 1996, Page(s):412  421
Cited by: Papers (6)A common subproblem of DNF approximate counting and derandomizing RL is the discrepancy problem for combinatorial rectangles. We explicitly construct a poly(n)size sample space that approximates the volume of any combinatorial rectangle in [n]^{n} to within o(1) error. The construction extends the previous techniques for the analogous hitting set problem, most notably via discrepancy pres... View full abstract»

Path coloring on the mesh
Publication Year: 1996, Page(s):400  409
Cited by: Papers (9)In the minimum path coloring problem, we are given a list of pairs of vertices of a graph. We are asked to connect each pair by a colored path. Paths of the same color must be edge disjoint. Our objective is to minimize the number of colors used. This problem was raised by A. Aggarwal et al. (1994) and P. Raghavan and E. Upfal (1994) as a model for routing in alloptical networks. It is also relat... View full abstract»

An efficient algorithm for constructing minimal trellises for codes over finite Abelian groups
Publication Year: 1996, Page(s):144  153We present an efficient algorithm for computing the minimal trellis for a group code over a finite Abelian group, given a generator matrix for the code. We also show how to compute a succinct representation of the minimal trellis for such a code, and present algorithms that use this information to efficiently compute local descriptions of the minimal trellis. This extends the work of Kschischang a... View full abstract»

Universal stability results for greedy contentionresolution protocols
Publication Year: 1996, Page(s):380  389
Cited by: Papers (20)  Patents (1)In this paper we analyze the behavior of communication networks in which packets are generated dynamically at the nodes and routed in discrete time steps across the edges. We focus on a basic adversarial model of packet generation and path determination for which the timeaveraged injection rate of packets requiring the use of any edge is limited to be less than 1. A crucial issue that arises in s... View full abstract»

Efficient information gathering on the Internet
Publication Year: 1996, Page(s):234  243
Cited by: Papers (9)The Internet offers unprecedented access to information. At present most of this information is free, but information providers ore likely to start charging for their services in the near future. With that in mind this paper introduces the following information access problem: given a collection of n information sources, each of which has a known time delay, dollar cost and probability of providin... View full abstract»

Approximate option pricing
Publication Year: 1996, Page(s):244  253As increasingly large volumes of sophisticated options are traded in world financial markets, determining a “fair” price for these options has become an important and difficult computational problem. Many valuation codes use the binomial pricing model, in which the stock price is driven by a random walk. In this model, the value of an nperiod option on a stock is the expected timedis... View full abstract»

Nearoptimal parallel prefetching and caching
Publication Year: 1996, Page(s):540  549
Cited by: Papers (8)  Patents (1)The authors consider algorithms for integrated prefetching and caching in a model with a fixedsize cache and any number of backing storage devices (disks). Previously, the single disk case was considered by Cao et al. (1995). They show that the natural extension of their aggressive algorithm to the parallel disk case is suboptimal by a factor near the number of disks in the worst case. The main r... View full abstract»

Short paths in expander graphs
Publication Year: 1996, Page(s):86  95
Cited by: Papers (12)Graph expansion has proved to be a powerful general tool for analyzing the behavior of routing algorithms and the interconnection networks on which they run. We develop new routing algorithms and structural results for boundeddegree expander graphs. Our results are unified by the fact that they are all based upon, and extend, a body of work: asserting that expanders are rich in short, disjoint p... View full abstract»

Approximate checking of polynomials and functional equations
Publication Year: 1996, Page(s):592  601
Cited by: Papers (1)The authors show how to check programs that compute polynomials and functions defined by addition theoremsin the realistic setting where the output of the program is approximate instead of exact. They present results showing how to perform approximate checking, selftesting, and selfcorrecting of polynomials, settling in the affirmative a question raised by Gemmell et al. (1991), and Rubinfeld a... View full abstract»

A 3approximation for the minimum tree spanning k vertices
Publication Year: 1996, Page(s):302  309
Cited by: Papers (11)In this paper we give a 3approximation algorithm for the problem of finding a minimum tree spanning any kvertices in a graph. Our algorithm extends to a 3approximation algorithm for the minimum tour that visits any kvertices View full abstract»

Faster deterministic sorting and searching in linear space
Publication Year: 1996, Page(s):135  141
Cited by: Papers (7)We present a significant improvement on linear space deterministic sorting and searching. On a unitcost RAM with word size w, an ordered set of n wbit keys (viewed as binary strings or integers) can be maintained in O(min{[√(logn)][logn/logw+loglogn][logwloglogn]}) time per operation, including insert, delete, member search, and neighbour search. The cost for searching is worstcase while ... View full abstract»

Approximate strip packing
Publication Year: 1996, Page(s):31  36
Cited by: Papers (9)We present an approximation scheme for strippacking, or packing rectangles into a rectangle of fixed width and minimum height, a classical NPhard cuttingstock problem. The algorithm finds a packing of n rectangles whose total height is within a factor of (1+ε) of optimal, and has running time polynomial both in n and in 1/ε. It is based on a reduction to fractional binpacking, and ca... View full abstract»

Verifying identities
Publication Year: 1996, Page(s):612  616The authors provide an O˜(n^{2}) time randomized algorithm to check whether a given operation f:S×S→S is associative (letting n=S). They prove this performance is optimal (up to polylogarithmic factors) even in case the operation is “cancellative”. No subn^{3} algorithm was previously known for this task. More generally they give an O(n^{c })... View full abstract»

New lower bounds for halfspace emptiness
Publication Year: 1996, Page(s):472  481The author derives a lower bound of Ω(n^{4/3}) for the halfspace emptiness problem: given a set of n points and n hyperplanes in
R ^{5}, is every point above every hyperplane? This matches the best known upper bound to within polylogarithmic factors, and improves the previous best lower bound of Ω(nlogn). The lower bound applies to partitioning algorithms in whi... View full abstract» 
Temporal logic and semidirect products: an effective characterization of the until hierarchy
Publication Year: 1996, Page(s):256  263
Cited by: Papers (4)We reveal an intimate connection between semidirect products of finite semigroups and substitution of formulas in linear temporal logic. We use this connection to obtain an algebraic characterization of the `until' hierarchy of linear temporal logic; the kth level of that hierarchy is comprised of all temporal properties that are expressible by a formula of nesting depth at most k in the `until' ... View full abstract»

Solving systems of polynomial congruences modulo a large prime
Publication Year: 1996, Page(s):115  124
Cited by: Papers (2)We consider the following polynomial congruences problem: given a prime p, and a set of polynomials f_{1},...,f_{m}∈
F _{p}[x_{1},...,x_{n}] of total degree at most d, solve the system f_{1}=...=f_{m}=0 for solution(s) inF _{p}^{n}. We give a randomized algorithm for the decision version of this problem. ... View full abstract» 
Optimal dynamic interval management in external memory
Publication Year: 1996, Page(s):560  569
Cited by: Papers (14)  Patents (1)The authors present a space and I/Ooptimal externalmemory data structure for answering stabbing queries on a set of dynamically maintained intervals. The data structure settles an open problem in databases and I/O algorithms by providing the first optimal externalmemory solution to the dynamic interval management problem, which is a special case of 2dimensional range searching and a central p... View full abstract»

Deterministic routing with bounded buffers: turning offline into online protocols
Publication Year: 1996, Page(s):370  379
Cited by: Papers (2)In this paper we present a deterministic protocol for routing arbitrary permutations in arbitrary networks. The protocol is analyzed in terms of the size of the network and the routing number of the network. Given a network H of size n, the routing number of H is defined as the maximum over all permutations π on [n] of the minimal number of steps to route π offline in H. We can show that for... View full abstract»

Learning linear transformations
Publication Year: 1996, Page(s):359  368
Cited by: Papers (9)We present a polynomial time algorithm to learn (in Valiant's PAC model) an arbitrarily oriented cube in nspace, given uniformly distributed sample points from it. In fact, we solve the more general problem of learning, in polynomial time, a linear (affine) transformation of a product distribution View full abstract»

A general approach to dynamic packet routing with bounded buffers
Publication Year: 1996, Page(s):390  399
Cited by: Papers (1)We prove a sufficient condition for the stability of dynamic packet routing algorithms. Our approach reduces the problem of steady state analysis to the easier and better understood question of static routing. We show that certain high probability and worst case bounds on the quasistatic (finite past) performance of a routing algorithm imply bounds on the performance of the dynamic version of that... View full abstract»

Simplified and improved resolution lower bounds
Publication Year: 1996, Page(s):274  282
Cited by: Papers (31)We give simple new lower bounds on the lengths of resolution proofs for the pigeonhole principle and for randomly generated formulas. For random formulas, our bounds significantly extend the range of formula sizes for which nontrivial lower bounds are known. For example, we show that with probability approaching 1, any resolution refutation of a randomly chosen 3CNF formula with at most n^{6/... View full abstract»}
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ISSN:
02725428
Subjects
 Computing & Processing