Solution of a divide-and-conquer maximin recurrence
SIAM Journal on Computing
Introduction to algorithms
Maintenance of a minimum spanning forest in a dynamic plane graph
Journal of Algorithms
Multidimensional Divide-and-Conquer Maximin Recurrences
SIAM Journal on Discrete Mathematics
Journal of Algorithms
Randomized dynamic graph algorithms with polylogarithmic time per operation
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
The homogeneous set sandwich problem
Information Processing Letters
An algorithmic view of gene teams
Theoretical Computer Science
Fast algorithms for identifying maximal common connected sets of interval graphs
Discrete Applied Mathematics
The pair completion algorithm for the homogeneous set sandwich problem
Information Processing Letters
Journal of Computer and System Sciences
Computing common intervals of K permutations, with applications to modular decomposition of graphs
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Revisiting t. uno and m. yagiura's algorithm
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Complexity issues for the sandwich homogeneous set problem
Discrete Applied Mathematics
Unique perfect phylogeny is NP-hard
CPM'11 Proceedings of the 22nd annual conference on Combinatorial pattern matching
Unique perfect phylogeny is intractable
Theoretical Computer Science
Hi-index | 5.23 |
We exemplify an optimization criterion for divide-and-conquer algorithms with a technique called generic competitive graph search. The technique is then applied to solve two problems arising from biocomputing, so-called Common Connected Components and Cograph Sandwich. The first problem can be defined as follows: given two graphs on the same set of n vertices, find the coarsest partition of the vertex set into subsets which induce connected subgraphs in both input graphs. The second problem is an instance of sandwich problems: given a partial subgraph G"1 of G"2, find a partial subgraph G of G"2 that is partial supergraph of G"1 (sandwich), and that is a cograph. For the former problem our generic algorithm not only achieves the current best known performance on arbitrary graphs and forests, but also improves by a logn factor when the input is made of planar graphs. However, our complexity for intervals graphs is slightly lower than a recent result. For the latter problem, we first study the relationship between the common connected components problem and the cograph sandwich problem, then, using our competitive graph search paradigm, we improve the computation of cograph sandwiches from O(n(n+m)) down to O(n+mlog^2n), where n is the number of vertices and m of total edges.