Maximum weight clique algorithms for circular-arc graphs and circle graphs
SIAM Journal on Computing
New clique and independent set algorithms for circle graphs
Discrete Applied Mathematics
Multidimensional divide-and-conquer
Communications of the ACM
Enumerating longest increasing subsequences and patience sorting
Information Processing Letters
Longest increasing subsequences in sliding windows
Theoretical Computer Science
All semi-local longest common subsequences in subquadratic time
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
Longest increasing subsequences in windows based on canonical antichain partition
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Space-Efficient and fast algorithms for multidimensional dominance reporting and counting
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Finding common structured patterns in linear graphs
Theoretical Computer Science
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
Common structured patterns in linear graphs: approximation and combinatorics
CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching
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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(n1.5) 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(n1.5). Compared to a number of previous algorithms for this problem, our approach presents a substantial improvement in worst-case running time.