2022 Nov. 1994
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Proceedings 35th Annual Symposium on Foundations of Computer Science
Publication Year: 1994 PDF (87 KB) 
Expander codes
Publication Year: 1994, Page(s):566  576
Cited by: Papers (9)  Patents (1)We present a new class of asymptotically good, linear errorcorrecting codes based upon expander graphs. These codes have linear time sequential decoding algorithms, logarithmic time parallel decoding algorithms with a linear number of processors, and are simple to understand. We present both randomized and explicit constructions for some of these codes. Experimental results demonstrate the extrem... View full abstract»

Efficient averagecase algorithms for the modular group
Publication Year: 1994, Page(s):143  152The modular group occupies a central position in many branches of mathematical sciences. In this paper we give average polynomialtime algorithms for the unbounded and bounded membership problems for finitely generated subgroups of the modular group. The latter result affirms a conjecture of Y. Gurevich (1990) View full abstract»

The geometry of graphs and some of its algorithmic applications
Publication Year: 1994, Page(s):577  591
Cited by: Papers (30)We explore some implications of viewing graphs as geometric objects. This approach offers a new perspective on a number of graphtheoretic and algorithmic problems. There are several ways to model graphs geometrically and our main concern here is with geometric representations that respect the metric of the (possibly weighted) graph. Given a graph G we map its vertices to a normed space in an atte... View full abstract»

Algebraic computation trees in characteristic p>0
Publication Year: 1994, Page(s):534  539
Cited by: Papers (1)We provide a simple and powerful combinatorial method for proving lower bounds for algebraic computation trees over algebraically closed fields of characteristic p>0. We apply our method to prove, for example, an Ω(n log n) lower bound for the n element distinctness problem, an Ω(n log(n/k)) lower bound to the “kequal problem”that is deciding whether there are k identi... View full abstract»

Finding the k shortest paths
Publication Year: 1994, Page(s):154  165
Cited by: Papers (120)  Patents (5)We give algorithms for finding the k shortest paths (not required to be simple) connecting a pair of vertices in a digraph. Our algorithms output an implicit representation of these paths in a digraph with n vertices and m edges, in time O(m+n log n+k). We can also find the k shortest paths from a given source s to each vertex in the graph, in total time O(m+n log n+kn). We describe applications t... View full abstract»

Tail bounds for occupancy and the satisfiability threshold conjecture
Publication Year: 1994, Page(s):592  603
Cited by: Papers (10)The classical occupancy problem is concerned with studying the number of empty bins resulting from a random allocation of m balls to n bins. We provide a series of tail bounds on the distribution of the number of empty bins. These tail bounds should find application in randomized algorithms and probabilistic analysis. Our motivating application is the following wellknown conjecture on threshold p... View full abstract»

An O(n^{1+ϵ} log b) algorithm for the complex roots problem
Publication Year: 1994, Page(s):540  547
Cited by: Papers (2)Given a univariate polynomial f(z) of degree n with complex coefficients, whose real and imaginary parts can be expressed as a ratio of two integers less than 2m in magnitude, the root problem is to find all the roots of f(z) up to specified precision 2μ . Assuming the arithmetic model for computation, we provide, for any ε>0, an algorithm which has complexity O(n... View full abstract»

Maximum agreement subtree in a set of evolutionary treesmetrics and efficient algorithms
Publication Year: 1994, Page(s):758  769
Cited by: Papers (3)  Patents (1)In this paper we prove that the maximum homeomorphic agreement subtree problem is 𝒩𝒫complete for three trees with unbounded degrees. We then show an approximation algorithm of time O(kn5) for choosing the species that are not in a maximum agreement subtree of a set of k trees. Our approximation is guaranteed to provide a set that is no more than 4 times the optimum solution. ... View full abstract»

“Go with the winners” algorithms
Publication Year: 1994, Page(s):492  501
Cited by: Papers (15)  Patents (1)We can view certain randomized optimization algorithms as rules for randomly moving a particle around in a state space; each state might correspond to a distinct solution to the optimization problem, or more generally, the state space might express some other structure underlying the optimization algorithm. In this setting, a general paradigm for designing heuristics is to run several simulations ... View full abstract»

CS proofs
Publication Year: 1994, Page(s):436  453
Cited by: Papers (27)This paper puts forward a computationallybased notion of proof and explores its implications to computation at large. In particular, given a random oracle or a suitable cryptographic assumption, we show that every computation possesses a short certificate vouching its correctness, and that, under a cryptographic assumption, any program for a 𝒩𝒫complete problem is checkable in polynomia... View full abstract»

Lower bounds on Hilbert's Nullstellensatz and propositional proofs
Publication Year: 1994, Page(s):794  806
Cited by: Papers (9)The weak form of the Hilbert's Nullstellensatz says that a system of algebraic equations over a field, Qi(x¯)=0, does not have a solution in the algebraic closure iff 1 is in the ideal generated by the polynomials Qi(x¯). We shall prove a lower bound on the degrees of polynomials Pi(x¯) such that Σ i Pi(x¯)Qi View full abstract»

Long tours and short superstrings
Publication Year: 1994, Page(s):166  177
Cited by: Papers (13)This paper considers weightmaximizing variants of the classical symmetric and asymmetric travelingsalesman problems. Like their weightminimizing counterparts, these variants are MAX SNPhard. We present the first nontrivial approximation algorithms for these problems. Our algorithm for directed graphs finds a tour whose weight is at least 38/63≈0.603 times the weight of a maximumweight tour... View full abstract»

Priority encoding transmission
Publication Year: 1994, Page(s):604  612
Cited by: Papers (31)  Patents (4)We introduce a novel approach for sending messages over lossy packetbased networks. The new method, called Priority Encoding Transmission, allows a user to specify a different priority on each segment of the message. Based on the priorities, the sender uses the system to encode the segments into packets for transmission. The system ensures recovery of the segments in order of their priority. The ... View full abstract»

Efficient oblivious branching programs for threshold functions
Publication Year: 1994, Page(s):309  317In his survey paper on branching programs, A.A. Razborov (1991) asked the following question: Does every rectifierswitching network computing the majority of n bits have size n1+Ω(1)? We answer this question in the negative by constructing a simple oblivious branching program of size O(n log3 n/log log n log log log n) for computing any threshold function. This improve... View full abstract»

Complexity lower bounds for computation trees with elementary transcendental function gates
Publication Year: 1994, Page(s):548  552
Cited by: Papers (1)We consider computation trees which admit as gate functions along with the usual arithmetic operations also algebraic or transcendental functions like exp, log, sin, square root (defined in the relevant domains) or much more general, Pfaffian functions. A new method for proving lower bounds on the depth of these trees is developed which allows to prove a lower bound Ω(√(log N)) for tes... View full abstract»

Optimal evolutionary tree comparison by sparse dynamic programming
Publication Year: 1994, Page(s):770  779
Cited by: Papers (6)In computational biology one is often interested in finding the concensus between different evolutionary trees for the same set of species. A popular formalizations is the Maximum Agreement Subtree Problem (MAST) defined as follows: given a set A and two rooted trees 𝒯0 and 𝒯1 leaflabeled by the elements of A, find a maximum cardinality subset B of A such that the ... View full abstract»

On the robustness of functional equations
Publication Year: 1994, Page(s):288  299
Cited by: Papers (2)Given a functional equation, such as ∀x, y f(x)+f(y)=f(x+y), we study the following general question: When can the “for all” quantifiers be replaced by “for most” quantifiers without essentially changing the functions that are characterized by the property? When “for most” quantifiers are sufficient, we say that the functional equation is robust. We show ... View full abstract»

Computing with very weak random sources
Publication Year: 1994, Page(s):264  275
Cited by: Papers (8)  Patents (2)For any fixed ε>0, we show how to simulate RP algorithms in time nO(log n) using the output of a δsource with minentropy R(ε). Such a weak random source is asked once for R(ε) bits; it outputs an Rbit string such that any string has probability at most 2R(ε). If ε>11/(k+1), our BPP simulations take time nO(log(k n)) (log
View full abstract» 
A spectral approach to lower bounds
Publication Year: 1994, Page(s):674  682
Cited by: Papers (2)We establish a nonlinear lower bound for halfplane range searching over a group. Specifically, we show that summing up the weights of n (weighted) points within n halfplanes requires Ω(n log n) additions and subtractions. This is the first nontrivial lower bound for range searching over a group. By constrast, range searching over a semigroup (which forbids subtractions) is almost completely ... View full abstract»

More outputsensitive geometric algorithms
Publication Year: 1994, Page(s):695  702
Cited by: Papers (17)A simple idea for speeding up the computation of extrema of a partially ordered set turns out to have a number of interesting applications in geometric algorithms; the resulting algorithms generally replace an appearance of the input size n in the running time by an output size A⩽n. In particular, the A coordinatewise minima of a set of n points in Rd can be found by an algorithm n... View full abstract»

Finding separator cuts in planar graphs within twice the optimal
Publication Year: 1994, Page(s):14  23
Cited by: Papers (2)Building on the works of S.B. Rao (1987, 1992) and J.K. Park and C.A. Phillips (1993), we present a factor 2 approximation algorithm for the problem of finding a minimum cost bbalanced cut in planar graphs, for b⩽1/3, if the vertex weights are given in unary (using scaling, a psuedoapproximation algorithm is also presented for the case of binary vertex weights). This problem is of considerab... View full abstract»

Randomized simplex algorithms on KleeMinty cubes
Publication Year: 1994, Page(s):502  510We investigate the behavior of randomized simplex algorithms on special linear programs. For this, we develop combinatorial models for the KleeMinty cubes (1972) and similar linear programs with exponential decreasing paths. The analysis of two most natural randomized pivot rules on the KleeMinty cubes leads to (nearly) quadratic lower bounds for the complexity of linear programming with random ... View full abstract»

On monotone formula closure of SZK
Publication Year: 1994, Page(s):454  465
Cited by: Papers (13)We investigate structural properties of statistical zero knowledge (SZK) both in the interactive and in the noninteractive model. Specifically, we look into the closure properties of SZK languages under monotone logical formula composition. This gives rise to new protocol techniques. We show that interactive SZK for random self reducible languages (RSR) (and for coRSR) is closed under monotone B... View full abstract»

Fast and lean selfstabilizing asynchronous protocols
Publication Year: 1994, Page(s):226  239
Cited by: Papers (7)We consider asynchronous general topology dynamic networks of identical nameless nodes with worstcase transient faults. Starting from any faulty configuration, our protocols selfstabilize any computation in time polynomial in the (unknown) network diameter. This version sacrifices some diversity of tasks and efficiency for simplicity and clarity of details. Appendix gives more efficient procedur... View full abstract»