scholarly journals Solving the Maximum Matching Problem on Bipartite <i>Star</i><sub>123</sub>-Free Graphs in Linear Time

2016 ◽  
Vol 06 (01) ◽  
pp. 13-24
Author(s):  
Ruzayn Quaddoura
Keyword(s):  
Linear Time ◽  
Maximum Matching ◽  
Matching Problem

A New Algorithm for Subset Matching Problem Based on Set-String Transformation

2009 ◽  
pp. 607-615
Author(s):  
Yangjun Chen
Keyword(s):  
Programming Languages ◽  
Linear Time ◽  
String Matching ◽  
Special Problem ◽  
Computer Engineering ◽  
Data Types ◽  
Matching Problem ◽  
Matching Problems ◽  
Abstract Data ◽  
Geometric Pattern Matching

In computer engineering, a number of programming tasks involve a special problem, the so-called tree matching problem (Cole & Hariharan, 1997), as a crucial step, such as the design of interpreters for nonprocedural programming languages, automatic implementation of abstract data types, code optimization in compilers, symbolic computation, context searching in structure editors and automatic theorem proving. Recently, it has been shown that this problem can be transformed in linear time to another problem, the so called subset matching problem (Cole & Hariharan, 2002, 2003), which is to find all occurrences of a pattern string p of length m in a text string t of length n, where each pattern and text position is a set of characters drawn from some alphabet S. The pattern is said to occur at text position i if the set p[j] is a subset of the set t[i + j - 1], for all j (1 = j = m). This is a generalization of the ordinary string matching and is of interest since an efficient algorithm for this problem implies an efficient solution to the tree matching problem. In addition, as shown in (Indyk, 1997), this problem can also be used to solve general string matching and counting matching (Muthukrishan, 1997; Muthukrishan & Palem, 1994), and enables us to design efficient algorithms for several geometric pattern matching problems. In this article, we propose a new algorithm on this issue, which needs only O(n + m) time in the case that the size of S is small and O(n + m·n0.5) time on average in general cases.

IDPM: An Improved Degenerate Pattern Matching Algorithm for Biological Sequences

2017 ◽  
Vol 28 (07) ◽  
pp. 889-914
Author(s):  
Jie Lin ◽  
Yue Jiang ◽  
E. James Harner ◽  
Bing-Hua Jiang ◽  
Don Adjeroh
Keyword(s):  
Performance Improvement ◽  
Pattern Matching ◽  
Linear Time ◽  
Computational Cost ◽  
Large Data ◽  
Biological Sequences ◽  
Matching Problem ◽  
Practical Utilization ◽  
Matching Algorithm ◽  
Pattern Matching Algorithm

Let [Formula: see text] be a string, with symbols from an alphabet. [Formula: see text] is said to be degenerate if for some positions, say [Formula: see text], [Formula: see text] can contain a subset of symbols from the symbol alphabet, rather than just one symbol. Given a text string [Formula: see text] and a pattern [Formula: see text], both with symbols from an alphabet [Formula: see text], the degenerate string matching problem, is to find positions in [Formula: see text] where [Formula: see text] occured, such that [Formula: see text], [Formula: see text], or both are allowed to be degenerate. Though some algorithms have been proposed, their huge computational cost pose a significant challenge to their practical utilization. In this work, we propose IDPM, an improved degenerate pattern matching algorithm based on an extension of the Boyer–Moore algorithm. At the preprocessing phase, the algorithm defines an alphabet-independent compatibility rule, and computes the shift arrays using respective variants of the bad character and good suffix heuristics. At the search phase, IDPM improves the matching speed by using the compatibility rule. On average, the proposed IDPM algorithm has a linear time complexity with respect to the text size, and to the overall size of the pattern. IDPM demonstrates significance performance improvement over state-of-the-art approaches. It can be used in fast practical degenerate pattern matching with large data sizes, with important applications in flexible and scalable searching of huge biological sequences.

scholarly journals Deterministic Dynamic Matching in O(1) Update Time

Algorithmica ◽  
2019 ◽  
Vol 82 (4) ◽  
pp. 1057-1080 ◽  
Author(s):  
Sayan Bhattacharya ◽  
Deeparnab Chakrabarty ◽  
Monika Henzinger
Keyword(s):  
Computer Science ◽  
Vertex Cover ◽  
Approximation Ratio ◽  
Approximate Algorithm ◽  
Maximum Matching ◽  
Matching Problem ◽  
Dynamic Algorithm ◽  
Dynamic Matching ◽  
Deterministic Dynamic ◽  
Oblivious Adversary

Abstract We consider the problems of maintaining an approximate maximum matching and an approximate minimum vertex cover in a dynamic graph undergoing a sequence of edge insertions/deletions. Starting with the seminal work of Onak and Rubinfeld (in: Proceedings of the ACM symposium on theory of computing (STOC), 2010), this problem has received significant attention in recent years. Very recently, extending the framework of Baswana et al. (in: Proceedings of the IEEE symposium on foundations of computer science (FOCS), 2011) , Solomon (in: Proceedings of the IEEE symposium on foundations of computer science (FOCS), 2016) gave a randomized dynamic algorithm for this problem that has an approximation ratio of 2 and an amortized update time of O(1) with high probability. This algorithm requires the assumption of an oblivious adversary, meaning that the future sequence of edge insertions/deletions in the graph cannot depend in any way on the algorithm’s past output. A natural way to remove the assumption on oblivious adversary is to give a deterministic dynamic algorithm for the same problem in O(1) update time. In this paper, we resolve this question. We present a new deterministic fully dynamic algorithm that maintains a O(1)-approximate minimum vertex cover and maximum fractional matching, with an amortized update time of O(1). Previously, the best deterministic algorithm for this problem was due to Bhattacharya et al. (in: Proceedings of the ACM-SIAM symposium on discrete algorithms (SODA), 2015); it had an approximation ratio of $$(2+\varepsilon )$$(2+ε) and an amortized update time of $$O(\log n/\varepsilon ^2)$$O(logn/ε2). Our result can be generalized to give a fully dynamic $$O(f^3)$$O(f3)-approximate algorithm with $$O(f^2)$$O(f2) amortized update time for the hypergraph vertex cover and fractional hypergraph matching problem, where every hyperedge has at most f vertices.

The Maximum Matching Problem Based on Self-Assembly Model of Molecular Beacon

2018 ◽  
Vol 10 (2) ◽  
pp. 213-218 ◽  
Author(s):  
Jing Yang ◽  
Zhixiang Yin ◽  
Kaifeng Huang ◽  
Jianzhong Cui
Keyword(s):  
Self Assembly ◽  
Molecular Beacon ◽  
Maximum Matching ◽  
Assembly Model ◽  
Matching Problem

Innovation of Matching Structures Through Clustering and Reconstructing Basic Operation Actions in the Form Layer

2017 ◽  
Author(s):  
Li Yu-Tong ◽  
Wang Yuxin
Keyword(s):  
Basic Mechanism ◽  
Maximum Matching ◽  
Basic Operation ◽  
Function Structure ◽  
Matching Problem ◽  
Direct Function ◽  
Matching Process ◽  
Order Relations ◽  
Functional Reasoning ◽  
Essential Knowledge

Due to a lack of essential knowledge to support functional reasoning from the design requirements of the kinematic compound mechanisms to their constituent mechanisms, the creative conceptual design of kinematic compound mechanisms based on functional synthesis approach is still a challenging task. Through introducing the dynamic partition-matching process between the function layer and the form layer to substitute for the direct function-structure matching in the FBS model, the function-structure matching problem corresponding to deficient functional reasoning knowledge for kinematic compound mechanisms is solved by the authors. The following challenge is how to cluster the divided subset of basic operation actions generated in the form layer during the partition-matching process into a well-organized and complete kinematic behavior that can be matched by the sub-function in the function layer and implemented by a structure in the database. The adopted strategies in this paper are: through defining the correlation indexes between basic operation actions, the basic operation action and its realized function behavior, and its embodied structure, as well as its dynamic behavior characteristics, the clustering possibility for a group of basic operation actions is determined. With the aid of the compatibility conditions between basic operation actions in the form layer and the consistency of the order relations between basic operation actions in the function layer and the form layer respectively, the consistency of the order relations among basic operation actions between the sub-functions in the function layer and the sub-behaviors in the form layer are guaranteed. Then, the optimal matching structures corresponding to the sub-functions in the function layer are determined based on the maximum matching coefficients of basic operation actions. In this way, the subsets of basic operation actions in the form layer are clustered into a number of complete behaviors that can be realized by mechanisms in the structure database and matched by the sub-functions in the function layer. Since multiple functional behaviors of each constituent basic mechanism take part in matching, some novel schemes of compound mechanisms with fewer and simpler constituent mechanisms to implement the overall function may be dug out.

scholarly journals On the Comparison Complexity of the String Prefix-Matching Problem

1995 ◽  
Vol 2 (46) ◽  
Author(s):  
Dany Breslauer ◽  
Livio Colussi ◽  
Laura Toniolo
Keyword(s):  
Linear Time ◽  
String Matching ◽  
Random Access ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Matching Problem ◽  
Machine Model ◽  
Worst Case ◽  
On Line ◽  
Sequential Comparison

In this paper we study the exact comparison complexity of the string<br />prefix-matching problem in the deterministic sequential comparison model<br />with equality tests. We derive almost tight lower and upper bounds on<br />the number of symbol comparisons required in the worst case by on-line<br />prefix-matching algorithms for any fixed pattern and variable text. Unlike<br />previous results on the comparison complexity of string-matching and<br />prefix-matching algorithms, our bounds are almost tight for any particular pattern.<br />We also consider the special case where the pattern and the text are the<br />same string. This problem, which we call the string self-prefix problem, is<br />similar to the pattern preprocessing step of the Knuth-Morris-Pratt string-matching<br />algorithm that is used in several comparison efficient string-matching<br />and prefix-matching algorithms, including in our new algorithm.<br />We obtain roughly tight lower and upper bounds on the number of symbol<br />comparisons required in the worst case by on-line self-prefix algorithms.<br />Our algorithms can be implemented in linear time and space in the<br />standard uniform-cost random-access-machine model.

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