Approximation algorithms
Linear structure of bipartite permutation graphs and the longest path problem
Information Processing Letters
Bioinformatics
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
The Longest Path Problem Is Polynomial on Interval Graphs
MFCS '09 Proceedings of the 34th International Symposium on Mathematical Foundations of Computer Science 2009
Efficient algorithms for the longest path problem
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
A linear time algorithm for the minimum spanning caterpillar problem for bounded treewidth graphs
SIROCCO'10 Proceedings of the 17th international conference on Structural Information and Communication Complexity
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We consider the problems of finding a caterpillar tree in a graph. We first prove that, unless P=NP, there is no approximation algorithms for finding a minimum spanning caterpillar in a graph within a factor of f(n); where f(n) is any polynomial time computable function of n, the order of the graph. Then we present a quadratic integer programming formulation for the problem that can be a base for a branch and cut algorithm. We also show that by using Gomory cuts iteratively, one can obtain a solution for the problem that is close to the optimal value by a factor of 1/ε, for 0