Faster exact algorithms for hard problems: A parameterized point of view

Faster Exa t Algorithms for Hard Problems : A Parameterized Point of View 1

Knapsack Problems: A Parameterized Point of View

The knapsack problem (KP) is a very famous NP-hard problem in combinatorial optimization. Also its generalization to multiple dimensions named d-dimensional knapsack problem (d-KP) and to multiple knapsacks named multiple knapsack problem (MKP) are well known problems. Since KP, d-KP, and MKP are integer-valued problems defined on inputs of various informations, we study the fixed-parameter tra...

Faster Exact Solutions for Some NP-Hard Problems

This paper considers a number of NP-complete problems, and provides faster algorithms for solving them. The solutions are based on a recursive partitioning of the problem domain, and careful elimination of some of the branches along the search without actually checking them. The time complexity of the proposed algorithms is of the form O(2 ) for constant 0¡ ¡ 1, where n is the output size of th...

Faster algorithms for vertex partitioning problems parameterized by clique-width

Many NP-hard problems, such as Dominating Set, are FPT parameterized by clique-width. For graphs of clique-width k given with a kexpression, Dominating Set can be solved in 4knO(1) time. However, no FPT algorithm is known for computing an optimal k-expression. For a graph of clique-width k, if we rely on known algorithms to compute a (23k − 1)expression via rank-width and then solving Dominatin...

Algorithms and experiments for parameterized approaches to hard graph problems

This thesis is about the design, analysis, implementation, and experimental evaluation of algorithms for hard graph problems. The aim is to establish that the concept of fixed-parameter tractability, and in particular novel algorithmic techniques whose development was driven by this concept, can lead to practically useful programs for exactly solving real-world problem instances. In particular,...