One of the most studied problems in combinatorial optimization is the maximum matching problem. A new technique for designing algorithms for finding maximum matchings is presented. This technique is based on finding t...
详细信息
In this paper, we consider the unordered pseudo-tree matching problem, which is a problem of, given two unordered labeled trees P and T, finding all occurrences of P in T via such many-to-one matchings that preserve n...
详细信息
The increase in huge amount of data is seen clearly in present days because of requirement for storing more information. To extract certain data from this large database is a very difficult task, including text proces...
详细信息
We address the issue of parallelizing constraint solvers based on local search methods for massively parallel architectures, involving several thousands of CPUs. We present a family of a constraint-based local search ...
详细信息
Randomizing polynomials represent a function f(x) by a low-degree randomized mapping p(x, r) over a finite field F such that, for any input x, the output distribution of p(x, r) depends only on the value of f(x). We s...
详细信息
ISBN:
(纸本)9781450311151
Randomizing polynomials represent a function f(x) by a low-degree randomized mapping p(x, r) over a finite field F such that, for any input x, the output distribution of p(x, r) depends only on the value of f(x). We study the class of functions f which admit an efficient representation by constant-degree randomizing polynomials. It is known that this class contains NC1 as well as log-space classes contained in NC2. Whether it contains all polynomial-time computable functions is a wide open question. A positive answer would have major and unexpected consequences, including the existence of efficient constant-round multiparty protocols with unconditional security, and the equivalence of (polynomial-time) cryptography and cryptography in NC 0. We obtain evidence for the limited power of randomizing polynomials by showing that a useful subclass of constant-degree randomizing polynomials cannot efficiently capture functions beyond NC. Concretely, we consider randomizing polynomials over fields F of a small characteristic in which each monomial has degree (at most) 2 in the random inputs r and constant degree in x. This subclass captures most constructions of randomizing polynomials from the literature. Our main result is that all functions f which can be efficiently represented by such randomizing polynomials over fields of a small characteristic are in non-uniform NC. (The same holds over arbitrary fields given a quadratic residuosity oracle.) This result is obtained in two steps: (1) we observe that computing f as above reduces to counting roots of degree-2 multivariate polynomials;(2) we design parallel algorithms for the latter problem. These parallel root counting algorithms may be of independent interest. On the flip side, our main result provides an avenue for obtaining new parallel algorithms via the construction of randomizing polynomials. This gives an unexpected application of cryptography to algorithm design. We provide several examples for the potential usef
Current languages for distributed memory machines tend to directly reflect the underlying hardware and thus provide little support for implementing data parallel algorithms. This paper describes a programming environm...
详细信息
parallel algorithms for ordered depth-first search (ODFS) and the monotone circuit value (MCV) on parallel random access machines (PRAMS) and single bus multiprocessors are presented. While it is known that these prob...
详细信息
Finding a minimum spanning tree of a graph is a well known problem in graph theory with many practical applications. We study serial variants of Prim's and Kruskal's algorithm and present their parallelization...
详细信息
ISBN:
(纸本)9789881925282
Finding a minimum spanning tree of a graph is a well known problem in graph theory with many practical applications. We study serial variants of Prim's and Kruskal's algorithm and present their parallelization targeting message passing parallel machine with distributed memory. We consider large graphs that can not fit into memory of one process. Experimental results show that Prim's algorithm is a good choice for dense graphs while Kruskal's algorithm is better for sparse ones. Poor scalability of Prim's algorithm comes from its high communication cost while Kruskal's algorithm showed much better scaling to larger number of processes.
We show how to test outerplanarity in time T(n)=O(lognlog n) using n/T(n) processors of CREW PRAM. It is the first optimal parallel algorithm recognizing a nontrivial class of graphs and it is the main result of the p...
详细信息
Two related results are presented. The first is a simple n/log n processor, O(log n) time parallel algorithm for list ranking. The second is a general parallel algorithmic technique for computations on trees;it yields...
详细信息
暂无评论