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) 
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 class NP contains exactly those languages L for which membership proofs (a proof that an input x is in L) 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 NP... View full abstract»

Proof verification and hardness of approximation problems
Publication Year: 1992, Page(s):14  23
Cited by: Papers (137)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»

Undirected connectivity in
Publication Year: 1992, Page(s):24  29O (log^{1.5}n ) space
Cited by: Papers (9)The authors present a deterministic algorithm for the connectivity problem on undirected graphs that runs in O(log^{1.5}n) space. Thus, the recursive doubling technique of Savich (1970) which requires Θ(log^{2}n) space is not optimal for this problem View full abstract»

The isomorphism conjecture holds relative to an oracle
Publication Year: 1992, Page(s):30  39
Cited by: Papers (9)The authors introduce symmetric perfect generic sets. these sets vary from the usual generic sets by allowing limited infinite encoding into the oracle. They then show that the BermanHartmanis (1977) isomorphism conjecture holds relative to any spgeneric oracle, i.e., for any symmetric perfect generic set A, all NPA complete sets are polynomialtime isomorphic relat... View full abstract»

The algorithmic aspects of the regularity lemma
Publication Year: 1992, Page(s):473  481
Cited by: Papers (5)The regularity lemma of Szemeredi (1978) is a result that asserts that every graph can be partitioned in a certain regular way. This result has numerous applications, but its known proof is not algorithmic. The authors first demonstrate the computational difficulty of finding a regular partition; they show that deciding if a given partition of an input graph satisfies the properties guaranteed by ... View full abstract»

On the bit extraction problem
Publication Year: 1992, Page(s):314  319
Cited by: Papers (16)Consider a coloring of the ndimensional Boolean cube with c=2s 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⩾θ c=(c/21)/(c1). This resolves the `bit extraction' or `tresilient functions' problem (also a special case of th... View full abstract»

Tiling a polygon with rectangles
Publication Year: 1992, Page(s):610  619
Cited by: Papers (9)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»

Data structural bootstrapping, linear path compression, and catenable heap ordered double ended queues
Publication Year: 1992, Page(s):40  49
Cited by: Papers (2)The authors provide an efficient implementation of catenable mindeques. To prove that the resulting data structure achieves constant amortized time per operation, they consider order preserving path compression. They prove a linear bound on deque ordered spineonly path compression, a case of order persevering path compression employed by the data structure View full abstract»

Dynamic halfspace reporting, geometric optimization, and minimum spanning trees
Publication Year: 1992, Page(s):80  89
Cited by: Papers (17)The authors describe dynamic data structures for halfspace range reporting and for maintaining the minima of a decomposable function. Using these data structures, they obtain efficient dynamic algorithms for a number of geometric problems, including closest/farthest neighbor searching, fixed dimension linear programming, bichromatic closest pair, diameter, and Euclidean minimum spanning tree View full abstract»

Enumerating the
Publication Year: 1992, Page(s):380  386k closest pairs optimally
Cited by: Papers (2)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 (_{2}^{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 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(n7log2 n) randomised algorithm to approximate the volume of a convex body, and an O(n6log n) algorithm to sample a point from the uniform distribution over a convex body. For convex polytopes the algorithm runs in O(n 7log4n) steps. Several t... 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(n2) time, but whose pattern processing is dependent on the alphabet and takes O(m2logΣ) time. The authors present an algorithm ... 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»

Back to the future: towards a theory of timed regular languages
Publication Year: 1992, Page(s):177  186
Cited by: Papers (6)The authors introduce twoway timed automatatimed automata that can move back and forth while reading a timed word. Twowayness in its unrestricted form leads, like nondeterminism, to the undecidability of language inclusion. However, if they restrict the number of times an input symbol may be revisited, then twowayness is both harmless and desirable. The authors show that the resulting class of... 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)2k; the authors complement this observation by proving that F ... View full abstract»

Fast algorithms for matrix normal forms
Publication Year: 1992, Page(s):121  130
Cited by: Papers (1)A Las Vegas type probabilistic algorithm is presented for computing the Frobenius normal form of an n×n matrix T over any field K. The algorithm requires O~(MM(n))=MM(n).(log n)O(1) operations in K, where O(MM(n)) operations in K are sufficient to multiply two n×n matrices over K. This nearly matches the lower bound of Ω(MM(n)) operations in K for... View full abstract»

Halvers and expanders [switching]
Publication Year: 1992, Page(s):686  692
Cited by: Papers (2)The authors investigate the asymptotic efficiency of certain combinatorial networks called halvers, which are basic building blocks of many parallel algorithms. They improve the efficiency of halvers in terms of their depth. The novelty is the use of combinatorial circuits whose basic units are ksorter switches View full abstract»

Witnesses for Boolean matrix multiplication and for shortest paths
Publication Year: 1992, Page(s):417  426
Cited by: Papers (10)The subcubic (O(nw) for w⟨3) algorithms to multiply Boolean matrices do not provide the witnesses; namely, they compute C=A·B but if Cij=1 they do not find an index k (a witness) such that Aik=Bkj=1. The authors design a deterministic algorithm for computing the matrix of witnesses that runs in O˜(nw) time, where here O&tilde... View full abstract»

Readthrice DNF is hard to learn with membership and equivalence queries
Publication Year: 1992, Page(s):523  532
Cited by: Papers (7)A general technique is developed to obtain nonlearnability results in the model of exact learning from equivalence and membership queries. The technique is applied to show that, assuming NP≠coNP, there does not exist a polynomialtime membership and equivalence query algorithm for exactly learning readthrice DNF formulasboolean formulas in disjunctive normal form where each variable appears ... View full abstract»

On the fault tolerance of some popular boundeddegree networks
Publication Year: 1992, Page(s):542  552
Cited by: Papers (19)The authors analyze the faulttolerance properties of several boundeddegree networks that are commonly used for parallel computation. Among other things, they show that an Nnode butterfly containing N1ε worstcase faults (for any constant ε>0) can emulate a faultfree butterfly of the same size with only constant slowdown. Similar results are proved for the shuf... View full abstract»

A theory of wormhole routing in parallel computers
Publication Year: 1992, Page(s):563  572
Cited by: Papers (14)Virtually all theoretical work on message routing in parallel computers has dwelt on packet routing: messages are conveyed as packets, an entire packet can reside at a node of the network, and a packet is sent from the queue of one node to the queue of another node until its reaches its destination. The current trend in multicomputer architecture, however, is to use wormhole routing. In wormhole r... 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»

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»

Fully dynamic biconnectivity in graphs
Publication Year: 1992, Page(s):50  59
Cited by: Papers (5)The author presents an algorithm for maintaining the biconnected components of a graph during a sequence of edge insertions and deletions. It requires linear storage and preprocessing time. The amortized running time for insertions and for deletions is O(m2/3 ), where m is the number of edges in the graph. Each query of the form `Are the vertices u and v biconnected?' can be answered i... View full abstract»