Improved Tree Decomposition Based Algorithms for Domination-like Problems

Improved Tree Decomposition Based Algorithms for Domination-like Problems

Branch and Tree Decomposition Techniques for Discrete Optimization

This chapter gives a general overview of two emerging techniques for discrete optimization that have footholds in mathematics, computer science, and operations research: branch decompositions and tree decompositions. Branch decompositions and tree decompositions along with their respective connectivity invariants, branchwidth and treewidth, were first introduced to aid in proving the Graph Mino...

Dynamic Programming on Tree Decompositions Using Generalised Fast Subset Convolution

In this paper, we show that algorithms on tree decompositions can be made faster with the use of generalisations of fast subset convolution. Amongst others, this gives algorithms that, for a graph, given with a tree decomposition of width k, solve the dominated set problem in O(nk3) time and the problem to count the number of perfect matchings in O∗(2k) time. Using a generalisation of fast subs...

Characterization of Efficiently Parallel Solvable

In this paper, we sketch common properties of a class of so-called subgraph optimization problems that can be systematically solved on distance-hereditary graphs. Based on the found properties, we then develop a general problem-solving paradigm that solves these problems efficiently in parallel. As a by-product, we also obtain new linear-time algorithms by a sequential simulation of our paralle...

A Hybrid MOEA/D-TS for Solving Multi-Objective Problems

In many real-world applications, various optimization problems with conflicting objectives are very common. In this paper we employ Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D), a newly developed method, beside Tabu Search (TS) accompaniment to achieve a new manner for solving multi-objective optimization problems (MOPs) with two or three conflicting objectives. This i...