AN IMPROVED PARALLEL ALGORITHM FOR A GEOMETRIC MATCHING PROBLEM WITH APPLICATION TO TRAPEZOID GRAPHS

We first design an 𝒪(n2) solution for finding a maximum induced matching in permutation graphs given their permutation models, based on a dynamic programming algorithm with the aid of the sweep line technique. With the support of the disjoint-set data structure, we improve the complexity to 𝒪(m+n). Consequently, we extend this result to give an 𝒪(m+n) algorithm for the same problem in trapezoid graphs. By combining our algorithms with the current best graph identification algorithms, we can solve the MIM problem in permutation and trapezoid graphs in linear and 𝒪(n2) time, respectively. Our results are far better than the best known 𝒪(mn) algorithm for the maximum induced matching problem in both graph classes, which was proposed by Habib et al.

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A parallel algorithm for solving the coloring problem on trapezoid graphs

Information Processing Letters ◽

10.1016/s0020-0190(97)00082-3 ◽

1997 ◽

Vol 62 (6) ◽

pp. 323-327 ◽

Cited By ~ 2

Author(s):

Shin-ichi Nakayama ◽

Shigeru Masuyama

Keyword(s):

Parallel Algorithm ◽

Coloring Problem ◽

Trapezoid Graphs

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Quadratic time algorithm for maximum induced matching problem in trapezoid graphs

Proceedings of the 2019 2nd International Conference on Information Science and Systems - ICISS 2019 ◽

10.1145/3322645.3322653 ◽

2019 ◽

Author(s):

Viet-Dung Nguyen ◽

Phan-Thuan Do

Keyword(s):

Time Algorithm ◽

Matching Problem ◽

Induced Matching ◽

Maximum Induced Matching ◽

Trapezoid Graphs

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A SPACE EFFICIENT BIT-PARALLEL ALGORITHM FOR THE MULTIPLE STRING MATCHING PROBLEM

International Journal of Foundations of Computer Science ◽

10.1142/s0129054106004388 ◽

2006 ◽

Vol 17 (06) ◽

pp. 1235-1251 ◽

Cited By ~ 1

Author(s):

DOMENICO CANTONE ◽

SIMONE FARO

Keyword(s):

Parallel Algorithms ◽

Parallel Algorithm ◽

Pattern Matching ◽

String Matching ◽

Common Factors ◽

Building Blocks ◽

Parallel Simulation ◽

Direct Simulation ◽

Matching Problem ◽

Multiple Pattern Matching

Finite (nondeterministic) automata are very useful building blocks in the field of string matching. This is particularly true in the case of multiple pattern matching, where the use of factor-based automata can reduce substantially the number of computational steps when the patterns have large common factors. Direct simulation of nondeterministic automata can be performed very efficiently using the bit-parallelism technique, though this is not necessarily true for factor-based automata. In this paper we present an algorithm for the multiple string matching problem, based on the bit-parallel simulation of nondeterministic factor-based automata which satisfy a particular ordering condition. We also show how to enforce such condition by suitably modifying a minimal initial automaton, through equivalence preserving transformations. The resulting automaton turns out to be smaller than the corresponding maximal automata used by existing bit-parallel algorithms, as they do not take any advantage of common factors in patterns.

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PARALLEL PATTERN MATCHING WITH SCALING

Parallel Processing Letters ◽

10.1142/s0129626401000476 ◽

2001 ◽

Vol 11 (01) ◽

pp. 125-138 ◽

Cited By ~ 1

Author(s):

H. MONGELLI ◽

S. W. SONG

Keyword(s):

Parallel Algorithms ◽

Parallel Algorithm ◽

Pattern Matching ◽

Computing Time ◽

Parallel Machine ◽

Experimental Results ◽

Coarse Grained ◽

Matching Problem ◽

Communication Round ◽

Parallel Pattern

Given a text and a pattern, the problem of pattern matching consists of determining all the positions of the text where the pattern occurs. When the text and the pattern are matrices, the matching is termed bidimensional. There are variations of this problem where we allow the matching using a somehow modified pattern. A modification that we will allow is that the pattern can be scaled. We propose a new parallel algorithm for this problem, under the CGM (Coarse Grained Multicomputer) model. This algorithm requires linear local computing time in the input, linear memory and uses only one communication round, during which at most a linear amount of data is exchanged. To be the best of our knowledge, there are no known parallel algorithms for the bidimensional pattern matching problem with scaling in the literature. This proposed algorithm was implemented in C, using the PVM interface and was executed on a Parsytec PowerXplorer parallel machine. The experimental results obtained were very promising and showed significant speedups.

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Using the Sadakane Compressed Suffix Tree to Solve the All-Pairs Suffix-Prefix Problem

BioMed Research International ◽

10.1155/2014/745298 ◽

2014 ◽

Vol 2014 ◽

pp. 1-11 ◽

Cited By ~ 3

Author(s):

Maan Haj Rachid ◽

Qutaibah Malluhi ◽

Mohamed Abouelhoda

Keyword(s):

Parallel Algorithm ◽

Suffix Tree ◽

De Novo ◽

Efficient Solutions ◽

Experimental Results ◽

Matching Problem ◽

De Novo Genome Assembly ◽

Large Size ◽

String Processing ◽

Compressed Index

The all-pairs suffix-prefix matching problem is a basic problem in string processing. It has an application in the de novo genome assembly task, which is one of the major bioinformatics problems. Due to the large size of the input data, it is crucial to use fast and space efficient solutions. In this paper, we present a space-economical solution to this problem using the generalized Sadakane compressed suffix tree. Furthermore, we present a parallel algorithm to provide more speed for shared memory computers. Our sequential and parallel algorithms are optimized by exploiting features of the Sadakane compressed index data structure. Experimental results show that our solution based on the Sadakane’s compressed index consumes significantly less space than the ones based on noncompressed data structures like the suffix tree and the enhanced suffix array. Our experimental results show that our parallel algorithm is efficient and scales well with increasing number of processors.

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