Journal of Discrete Algorithms
A measure & conquer approach for the analysis of exact algorithms
Journal of the ACM (JACM)
Polynomial-time solvability of the maximum clique problem
ECC'09 Proceedings of the 3rd international conference on European computing conference
Improved upper bounds for vertex cover
Theoretical Computer Science
A note on vertex cover in graphs with maximum degree 3
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Exact and parameterized algorithms for edge dominating set in 3-degree graphs
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
3-Hitting set on bounded degree hypergraphs: upper and lower bounds on the kernel size
TAPAS'11 Proceedings of the First international ICST conference on Theory and practice of algorithms in (computer) systems
Maximum independent set in graphs of average degree at most three in O(1.08537n)
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Fixed-parameter approximation: conceptual framework and approximability results
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
A simple and fast algorithm for maximum independent set in 3-degree graphs
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
Theoretical Computer Science
A novel parameterised approximation algorithm for minimum vertex cover
Theoretical Computer Science
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A sequence of exact algorithms to solve the Vertex Cover and Maximum Independent Set problems have been proposed in the literature. All these algorithms appeal to a very conservative analysis that considers the size of the search tree, under a worst-case scenario, to derive an upper bound on the running time of the algorithm. In this paper we propose a different approach to analyze the size of the search tree. We use amortized analysis to show how simple algorithms, if analyzed properly, may perform much better than the upper bounds on their running time derived by considering only a worst-case scenario. This approach allows us to present a simple algorithm of running time O(1.194kk2 + n) for the parameterized Vertex Cover problem on degree-3 graphs, and a simple algorithm of running time O(1.1255n) for the Maximum Independent Set problem on degree-3 graphs. Both algorithms improve the previous best algorithms for the problems.