Computational geometry: an introduction
Computational geometry: an introduction
Text algorithms
Perspectives of Monge properties in optimization
Discrete Applied Mathematics
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
SIAM Journal on Computing
Multidimensional divide-and-conquer
Communications of the ACM
A guided tour to approximate string matching
ACM Computing Surveys (CSUR)
On the common substring alignment problem
Journal of Algorithms
A Subquadratic Sequence Alignment Algorithm for Unrestricted Scoring Matrices
SIAM Journal on Computing
Space-Efficient and fast algorithms for multidimensional dominance reporting and counting
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Semi-local longest common subsequences in subquadratic time
Journal of Discrete Algorithms
Efficient representations of row-sorted 1-variant matrices for parallel string applications
ICA3PP'07 Proceedings of the 7th international conference on Algorithms and architectures for parallel processing
Fast distance multiplication of unit-Monge matrices
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Longest common subsequences in permutations and maximum cliques in circle graphs
CPM'06 Proceedings of the 17th Annual conference on Combinatorial Pattern Matching
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For two strings a, b of lengths m, n respectively, the longest common subsequence (LCS) problem consists in comparing a and b by computing the length of their LCS . In this paper, we define a generalisation, called “the all semi-local LCS problem”, where each string is compared against all substrings of the other string, and all prefixes of each string are compared against all suffixes of the other string. An explicit representation of the output lengths is of size Θ ((m+n)2). We show that the output can be represented implicitly by a geometric data structure of size O(m+n), allowing efficient queries of the individual output lengths. The currently best all string-substring LCS algorithm by Alves et al. can be adapted to produce the output in this form. We also develop the first all semi-local LCS algorithm, running in time o(mn) when m and n are reasonably close. Compared to a number of previous results, our approach presents an improvement in algorithm functionality, output representation efficiency, and/or running time.