2427 Oct. 1992
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Witnesses for Boolean matrix multiplication and for shortest paths
Publication Year: 1992, Page(s):417  426
Cited by: Papers (12)The subcubic (O(n/sup w/) for w(3) algorithms to multiply Boolean matrices do not provide the witnesses; namely, they compute C=A.B but if C/sub ij/=1 they do not find an index k (a witness) such that A/sub ik/=B/sub kj/=1. The authors design a deterministic algorithm for computing the matrix of witnesses that runs in O(n/sup w/) time, where here O(n/sup w/) denotes O(n/sup w/(log n)/sup O(1)/). T... View full abstract»

Towards a computational theory of statistical tests
Publication Year: 1992, Page(s):406  416
Cited by: Papers (3)The authors initiate a computational theory of statistical tests. Loosely speaking, an algorithm is a statistical test if it rejects a 'negligible' fraction of strings. A statistical test is universal for a class of algorithms if it rejects all (but finitely many) of the strings rejected by each algorithm in the class. They consider the existence and efficiency of universal statistical tests for v... View full abstract»

On minimum and maximum spanning trees of linearly moving points
Publication Year: 1992, Page(s):396  405
Cited by: Papers (2)The authors investigate the upper bounds on the numbers of transitions of minimum and maximum spanning trees (MinST and MaxST for short) for linearly moving points. Suppose that one is given a set of n points in general ddimensional space, S=(p/sub 1/,p/sub 2/, . . ., p/sub n/), and that all points move along different straight lines at different but fixed speeds, i.e., the position of p/sub i/ i... View full abstract»

Safe and effective determinant evaluation
Publication Year: 1992, Page(s):387  395
Cited by: Papers (23)The problem of evaluating the sign of the determinant of a small matrix aries in many geometric algorithms. Given an n*n matrix A with integer entries, whose columns are all smaller than M in Euclidean norm, the algorithm given evaluates the sign of the determinant det A exactly. The algorithm requires an arithmetic precision of less than 1.5n+2lgM bits. The number of arithmetic operations needed ... View full abstract»

Enumerating the k closest pairs optimally
Publication Year: 1992, Page(s):380  386
Cited by: Papers (3)Let S be a set of n points in Ddimensional space, where D is a constant, and let k be an integer between 1 and (/sub 2//sup n/) An algorithm is given that computes the k closest pairs in the set S in O(nlogn+k) time, using O(n+k) space. The algorithm fits in the algebraic decision tree model and is, therefore, optimal.<<ETX>> View full abstract»

On the completeness of objectcreating query languages
Publication Year: 1992, Page(s):372  379
Cited by: Papers (3)Recently, various database query languages have been considered that have the ability to create new domain elements. These languages, however, are not complete in the sense of Abiteboul and Kanellakis (1989). They provide a precise characterization for the class of queries that can be expressed in these languages. They call this class the constructive queries and motivate this term by establishing... View full abstract»

Efficient inference of partial types
Publication Year: 1992, Page(s):363  371
Cited by: Papers (3)  Patents (1)Partial types for the lambda calculus were introduced by Thatte (1988) as a means of typing objects that are not typable with simple types, such as heterogeneous lists and persistent data. He showed that type inference for partial types was semidecidable. Decidability remained open until O'Keefe and Wand gave an exponential time algorithm for type inference. The authors give an O(n/sup 3/) algori... View full abstract»

Undecidability of the Hornclause implication problem
Publication Year: 1992, Page(s):354  362
Cited by: Papers (8)The authors prove that the problem 'given two Horn clauses H/sub 1/=( alpha /sub 1/ Vproduct alpha /sub 2/ to beta ) and H/sub 2/=( gamma /sub 1/ Vproduct . . . Vproduct gamma /sub k/ to delta ), where alpha /sub i/, beta , gamma /sub i/, delta are atomic formulas, decide if H/sub 2/, is a consequence of H/sub 1/' is not recursive. This solves one of the last open decidability problems concerni... View full abstract»

The distributed kserver problema competitive distributed translator for kserver algorithms
Publication Year: 1992, Page(s):344  353
Cited by: Papers (7)  Patents (2)The authors consider the kserver problem in a distributed setting. Given a network of n processors, and k identical mobile servers, requests for service appear at the processors and a server must reach the request point. Besides modeling problems in computer networks where k identical mobile resources are shared by the processors of the network, this models a realistic situation where the transfe... View full abstract»

Lower bounds on the competitive ratio for mobile user tracking and distributed job scheduling
Publication Year: 1992, Page(s):334  343
Cited by: Papers (7)The authors prove a lower bound of Omega (log n/log log n) on the competitive ratio of any (deterministic or randomised) distributed algorithm for solving the mobile user problem on certain networks of n processors. The lower bound holds for various networks, including the hypercube, any network with sufficiently large girth, and any highly expanding graph. A similar Omega (log n/log log n) lower ... View full abstract»

Competitive analysis of financial games
Publication Year: 1992, Page(s):327  333
Cited by: Papers (22)In the unidirectional conversion problem an online player is given the task of converting dollars to yen over some period of time. Each day, a new exchange rate is announced and the player must decide how many dollars to convert. His goal is to minimize the competitive ratio. defined as sup/sub E/ (P/sub OPT/(E)/P/sub X/E) where E ranges over exchange rate sequences. P/sub OPT/(E) is the number o... View full abstract»

A mildly exponential approximation algorithm for the permanent
Publication Year: 1992, Page(s):320  326
Cited by: Papers (4)An approximation algorithm for the permanent of an n*n 0,1matrix is presented. The algorithm is shown to have worstcase time complexity exp (0(n/sup 1/2/ log/sup 2/ n)). Asymptotically, this represents a considerable improvement over the best existing algorithm, which has worstcase time complexity of the form e/sup theta (n)/.<<ETX>> View full abstract»

On the bit extraction problem
Publication Year: 1992, Page(s):314  319
Cited by: Papers (18)Consider a coloring of the ndimensional Boolean cube with c=2/sup s/ colors in such a way that every kdimensional subcube is equicolored, i.e. each color occurs the same number of times. The author shows that for such a coloring one necessarily has (k1)/n>or= theta /sub c/=(c/21)/(c1). This resolves the 'bit extraction' or 'tresilient functions' problem (also a special case of the privacy... View full abstract»

Quadratic dynamical systems
Publication Year: 1992, Page(s):304  313
Cited by: Papers (9)The paper promotes the study of computational aspects, primarily the convergence rate, of nonlinear dynamical systems from a combinatorial perspective. The authors identify the class of symmetric quadratic systems. Such systems have been widely used to model phenomena in the natural sciences, and also provide an appropriate framework for the study of genetic algorithms in combinatorial optimisatio... View full abstract»

On the second eigenvalue and linear expansion of regular graphs
Publication Year: 1992, Page(s):296  303
Cited by: Papers (5)The authors investigate the relation between the second eigenvalue and the linear expansion of regular graphs. The spectral method is the best currently known technique to prove lower bounds on the expansion. He improves this technique by showing that the expansion coefficient of linearsized subsets of a kregular graph G is at least k/2(1 square root max(0,1/sub lambda 1(G)2//sup 4k4/))/sup ... View full abstract»

Lower bounds on the depth of monotone arithmetic computations
Publication Year: 1992, Page(s):288  295
Cited by: Papers (1)Consider an arithmetic expression of length n involving only the operations (+,*) and nonnegative constants. The authors prove lower bounds on the depth of any binary computation tree over the same set of operations and constants that computes such an expression. In their main result they exhibit a family of arithmetic expressions that requires computation trees of depth at least 1.5 log/sub 2/n... View full abstract»

Separating the communication complexities of MOD m and MOD p circuits
Publication Year: 1992, Page(s):278  287The author proves in this paper that it is much harder to evaluate depth2, sizeN circuits with MOD m gates than with MOD p gates by kparty communication protocols: he shows a kparty protocol which communicates O(1) bits to evaluate circuits with MOD p gates, while evaluating circuits with MOD m gates needs Omega (N) bits, where p denotes a prime, and m a composite, nonprime power number. As a... View full abstract»

Algebraic decision trees and Euler characteristics
Publication Year: 1992, Page(s):268  277
Cited by: Papers (1)For any set S contained in R/sup n/, let chi (S) denote its Euler characteristic. The author shows that any algebraic computation tree or fixeddegree algebraic decision tree must have height Omega (log mod chi (S) mod )for deciding the membership question of a compact semialgebraic set S. This extends a result by A. Bjorner, L. Lovasz and A. Yao where it was shown that any linear decision tree f... View full abstract»

Amplification and percolation (probabilistic Boolean functions)
Publication Year: 1992, Page(s):258  267
Cited by: Papers (3)The authors extend R.B. Boppana's results (1989) in two ways. They first show that his two lower bounds hold for general readonce formulae, not necessarily monotone, that may even include exclusiveor gates. They are then able to join his two lower bounds together and show that any readonce, not necessarily monotone, formula that amplifies (p/sup 1///sub n/,p+/sup 1///sub n/) to (2/sup n/,12/... View full abstract»

Truly alphabetindependent twodimensional pattern matching
Publication Year: 1992, Page(s):247  256
Cited by: Papers (14)A. Amir, G. Benson and M. Farach (see Proc. 24th STOC, p.5968 (1992)) gave an algorithm for twodimensional pattern matching (ABF for short) whose text processing is independent of the alphabet and takes O(n/sup 2/) time, but whose pattern processing is dependent on the alphabet and takes O(m/sup 2/log mod Sigma mod ) time. The authors present an algorithm that is truly independent of the alphabe... View full abstract»

The asymptotic complexity of merging networks
Publication Year: 1992, Page(s):236  246
Cited by: Papers (1)Let M(m,n) be the minimum number of comparators needed in a comparator network that merges m elements x/sub 1/<or=x/sub 2/<or=. . .<or=x/sub m/ and n elements y/sub 1/<or=y/sub 2/. . .<or=y/sub n/, where n>or=m. Batcher's oddeven merge yields the following upper bound: M(m,n)<or=/sup 1///sub 2/(m+n)log/sub 2/(m+1)+O(n); in particular, M(n,n)<or=nlog/sub 2/n+O(n). The autho... View full abstract»

Improved lower bounds for Shellsort
Publication Year: 1992, Page(s):226  235
Cited by: Papers (2)The authors give improved lower bounds for Shellsort based on a new and relatively simple proof idea. The lower bounds obtained are both stronger and more general than the previously known bounds. In particular, they hold for nonmonotone increment sequences and adaptive Shellsort algorithms, as well as for some recently proposed variations of Shellsort.<<ETX>> View full abstract»

Online load balancing
Publication Year: 1992, Page(s):218  225
Cited by: Papers (22)The setup for the authors' problem consists of n servers that must complete a set of tasks. Each task can be handled only by a subset of the servers, requires a different level of service, and once assigned can not be reassigned. They make the natural assumption that the level of service is known at arrival time, but that the duration of service is not. The online load balancing problem is to as... View full abstract»

Markov paging
Publication Year: 1992, Page(s):208  217
Cited by: Papers (22)This paper considers the problem of paging under the assumption that the sequence of pages accessed is generated by a Markov chain. The authors use this model to study the faultrate of paging algorithms, a quantity of interest to practitioners. They first draw on the theory of Markov decision processes to characterize the paging algorithm that achieves optimal faultrate on any Markov chain. They... View full abstract»

A decomposition theorem and bounds for randomized server problems
Publication Year: 1992, Page(s):197  207
Cited by: Papers (6)The authors prove a lower bound of Omega ( square root logk/loglogk) for the competitive ratio of randomized algorithms for the kserver problem against an oblivious adversary. The bound holds for arbitrary metric spaces (of at least k+1 points) and provides a new lower bound for the metrical task system problem as well. This improves the previous best lower bound of Omega (loglogk) for arbitrary ... View full abstract»