Computational geometry: an introduction
Computational geometry: an introduction
Text algorithms
Perspectives of Monge properties in optimization
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Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
String editing and longest common subsequences
Handbook of formal languages, vol. 2
SIAM Journal on Computing
Bounds on the Complexity of the Longest Common Subsequence Problem
Journal of the ACM (JACM)
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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
An all-substrings common subsequence algorithm
Discrete Applied Mathematics
All semi-local longest common subsequences in subquadratic time
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
New algorithms for efficient parallel string comparison
Proceedings of the twenty-second annual ACM symposium on Parallelism in algorithms and architectures
Fast distance multiplication of unit-Monge matrices
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Parallel longest increasing subsequences in scalable time and memory
PPAM'09 Proceedings of the 8th international conference on Parallel processing and applied mathematics: Part I
Multiplication algorithms for Monge matrices
SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
Towards approximate matching in compressed strings: local subsequence recognition
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Note: A fast algorithm for multiplying min-sum permutations
Discrete Applied Mathematics
Monge properties of sequence alignment
Theoretical Computer Science
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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 @Q((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., based on previous work by Schmidt, 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.