Longest common subsequences in permutations and maximum cliques in circle graphs
Tiskin, Alexander (2006) Longest common subsequences in permutations and maximum cliques in circle graphs. In: 17th Annual Symposium on Combinatorial Pattern Matching, Tech Univ Catolonia, Barcelona, SPAIN, JUL 05-07, 2006. Published in: COMBINATORIAL PATTERN MATCHING, PROCEEDINGS, 4009 pp. 270-281.Full text not available from this repository.
For two strings a, b, the longest common subsequence (LCS) problem consists in comparing a and b by computing the length of their LCS. In a previous paper, we defined a generalisation, called "the all semi-local LCS problem", for which we proposed an efficient output representation and an efficient algorithm. In this paper, we consider a restriction of this problem to strings that are permutations of a given set. The resulting problem is equivalent to the all local longest increasing subsequences (LIS) problem. We propose an algorithm for this problem, running in time O(n(1.5)) on an input of size n. As an interesting application of our method, we propose a new algorithm for finding a maximum clique in a circle graph on n nodes, running in the same asymptotic time O(n(1.5)). Compared to a number of previous algorithms for this problem, our appreach presents a substantial improvement in worst-case running time.
|Item Type:||Conference Item (UNSPECIFIED)|
|Subjects:||Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software|
|Series Name:||LECTURE NOTES IN COMPUTER SCIENCE|
|Journal or Publication Title:||COMBINATORIAL PATTERN MATCHING, PROCEEDINGS|
|Editor:||Lewenstein, M and Valiente, G|
|Number of Pages:||12|
|Page Range:||pp. 270-281|
|Title of Event:||17th Annual Symposium on Combinatorial Pattern Matching|
|Location of Event:||Tech Univ Catolonia, Barcelona, SPAIN|
|Date(s) of Event:||JUL 05-07, 2006|
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