2427 Oct. 1992
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Proceedings 33rd Annual Symposium on Foundations of Computer Science (Cat. No.92CH31880)
Publication Year: 1992 PDF (83 KB) 
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 View full abstract»

Tighter bounds on the exact complexity of string matching
Publication Year: 1992, Page(s):600  609
Cited by: Papers (5)The paper considers how many character comparisons are needed to find all occurrences of a pattern of length m in a text of length n. The main contribution is to show an upper bound of the form n + O(n/m) character comparisons, following preprocessing. Specifically, the authors show an upper bound of n+8/3(m+1)(nm) character comparisons. This bound is achieved by an online algorithm which perform... View full abstract»

The asymptotic complexity of merging networks
Publication Year: 1992, Page(s):236  246Let
M (m ,n ) be the minimum number of comparators needed in a comparator network that mergesm elementsx _{1}⩽x _{2}⩽. . .⩽x _{m} andn elementsy _{1 }⩽y _{2}. . .⩽y _{n}, wheren ⩾m . Batcher's oddeven merge yields th... View full abstract» 
Tiling a polygon with rectangles
Publication Year: 1992, Page(s):610  619
Cited by: Papers (8)The authors study the problem of tiling a simple polygon of surface n with rectangles of given types (tiles). They present a linear time algorithm for deciding if a polygon can be tiled with 1 × m and k × 1 tiles (and giving a tiling when it exists), and a quadratic algorithm for the same problem when the tile types are m × k and k × m View full abstract»

Probabilistic checking of proofs; a new characterization of NP
Publication Year: 1992, Page(s):2  13
Cited by: Papers (62)The authors give a new characterization of
NP : the classNP contains exactly those languagesL for which membership proofs (a proof that an inputx is inL ) can be verified probabilistically in polynomial time using logarithmic number of random bits and sublogarithmic number of queries to the proof. This is a nonrelativizing characterization of ... View full abstract» 
Reconstructing algebraic functions from mixed data
Publication Year: 1992, Page(s):503  512
Cited by: Papers (12)  Patents (1)The authors consider the task of reconstructing algebraic functions given by black boxes. Unlike traditional settings, they are interested in black boxes which represent several algebraic functions
f _{1}, . . .,f _{k}, where at each inputx , the box arbitarrily chooses a subset off _{1}(x ), . . .,f _{k}(... View full abstract» 
Separating the communication complexities of MOD
Publication Year: 1992, Page(s):278  287m and MODp circuitsThe author proves in this paper that it is much harder to evaluate depth2, size
N circuits with MODm gates than with MODp gates byk party communication protocols: he shows ak party protocol which communicatesO (1) bits to evaluate circuits with MODp gates, while evaluating circuits with MODm gates needs Ω(... View full abstract» 
Randomized geometric algorithms and pseudorandom generators
Publication Year: 1992, Page(s):90  100
Cited by: Papers (2)The so called randomized incremental algorithms in computational geometry can be thought of as a generalization of Quicksort to higher dimensional geometric problems. They all construct the geometric complex in the given problem, such as a Voronoi diagram or a convex polytope, by adding the objects in the input set, one at a time, in a random order. The author shows that the expected running times... 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^{1/2} log^{2} n)). Asymptotically, this represents a considerable improvement over the best existing algorithm, which has worstcase time complexity of the form e^{θ(n)} View full abstract»

Truly alphabetindependent twodimensional pattern matching
Publication Year: 1992, Page(s):247  256
Cited by: Papers (12)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 ^{2}) time, but whose pattern processing is dependent on the alphabet and takesO (m ^{2}logΣ) time. The authors present an algorithm ... View full abstract» 
Mick gets some (the odds are on his side) [satisfiability]
Publication Year: 1992, Page(s):620  627
Cited by: Papers (37)  Patents (1)Consider a randomly generated boolean formula F (in the conjunctive normal form) with m clauses of size k over n variables; k is fixed at any value greater than 1, but n tends to infinity and m = (1 + o(1))cn for some c depending only on k. It is easy to see that F is unsatisfiable with probability 1o(1) whenever c>(ln 2)2^{k}; the authors complement this observation by proving that F ... View full abstract»

Randomized consensus in expected
Publication Year: 1992, Page(s):137  146O (n log^{2 }n ) operations per processorThe paper presents a new randomized algorithm for achieving consensus among asynchronous processors that communicate by reading and writing shared registers. The fastest previously known algorithm requires a processor to perform an expected
O (n ^{2 } logn ) read and write operations in the worst case. In the algorithm, each processor executes at most an expected ... View full abstract» 
Proof verification and hardness of approximation problems
Publication Year: 1992, Page(s):14  23
Cited by: Papers (136)The class PCP(f(n),g(n)) consists of all languages L for which there exists a polynomialtime probabilistic oracle machine that used O(f(n)) random bits, queries O(g(n)) bits of its oracle and behaves as follows: If x∈L then there exists an oracle y such that the machine accepts for all random choices but if x∉L then for every oracle y the machine rejects with high probability. Arora an... View full abstract»

Approximate max flow on small depth networks
Publication Year: 1992, Page(s):648  658
Cited by: Papers (1)The author considers the maximum flow problem on directed acyclic networks with m edges and depth r (length of the longest st path). The main result is a new deterministic algorithm for solving the relaxed problem of computing an st flow of value at least (1ε) of the maximum flow. For instances where r and ε^{1} are small (i.e., O(polylog(m))), this algorithm is in NC and use... View full abstract»

On the exact learning of formulas in parallel
Publication Year: 1992, Page(s):513  522
Cited by: Papers (3)The authors investigate the parallel complexity of learning formulas from membership and equivalence queries. They consider a number of learning problems that can be solved sequentially in polynomial time. They prove some upper and lower bounds on the number of parallel steps required to solve these problems with a polynomial number of processors 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... View full abstract» 
Drawing planar graphs using the
Publication Year: 1992, Page(s):101  110lmc ordering
Cited by: Papers (3)The author introduces a method to optimize the required area, minimum angle and number of bends of planar drawings of graphs on a grid. The main tool is a new type of ordering on the vertices and faces of triconnected planar graphs. With this method linear time and space algorithms can be designed for many graph drawing problems. He shows that every triconnected planar graph G can be drawn convexl... View full abstract»

How to denest Ramanujan's nested radicals
Publication Year: 1992, Page(s):447  456
Cited by: Papers (1)The author presents a simple condition when nested radical expressions of depth two can be denested using real radicals or radicals of some bounded degree. He describes the structure of these denestings and determines an upper bound on the maximum size of a denesting. Also for depth two radicals he describes an algorithm that will find such a denesting whenever one exists. Unlike all previous dene... View full abstract»

Competitive analysis of financial games
Publication Year: 1992, Page(s):327  333
Cited by: Papers (16)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_{E} (P_{OPT}(E)/P_{X}E) where E ranges over exchange rate sequences. P... View full abstract»

Markov paging
Publication Year: 1992, Page(s):208  217
Cited by: Papers (20)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»

Efficient minimum cost matching using quadrangle inequality
Publication Year: 1992, Page(s):583  592
Cited by: Papers (1)The authors present efficient algorithms for finding a minimum cost perfect matching, and for solving the transportation problem in bipartite graphs, G = (Red ∪ Blue, Red × Blue), where Red = n, Blue = m, n ⩽ m, and the cost function obeys the quadrangle inequality. The first results assume that all the red points and all the blue points lie on a curve that is homeomorphic to eit... View full abstract»

On the randomized complexity of volume and diameter
Publication Year: 1992, Page(s):482  492
Cited by: Papers (7)The authors give an
O (n ^{7}log^{2 }n ) randomised algorithm to approximate the volume of a convex body, and anO (n ^{6}logn ) algorithm to sample a point from the uniform distribution over a convex body. For convex polytopes the algorithm runs inO (n ^{7}log^{4}n ) steps. Several t... 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 ^{1}/_{n},p +... View full abstract» 
On fourconnecting a triconnected graph
Publication Year: 1992, Page(s):70  79
Cited by: Papers (5)  Patents (3)The author considers the problem of finding a smallest set of edges whose addition fourconnects a triconnected graph. This is a fundamental graphtheoretic problem that has applications in designing reliable networks. He presents an O(nα(m,n)+m) time sequential algorithm for fourconnecting an undirected graph G that is triconnected by adding the smallest number of edges, where n and m are ... View full abstract»