Average-case complexity of a branch-and-bound algorithm for MIN DOMINATING SET
Authors
Denat, T.; Harutyunyan, A.; Melissinos, N.; Paschos, V. T..
Year
2024
Published
Discrete Applied Mathematics. 2024, 345 4-8. ISSN 0166-218X.
Type
Article
Departments
Annotation
The average-case complexity of a branch-and-bound algorithm for MIN DOMINATING SET problem in random graphs in the G(n, p) model is studied. We identify phase transitions between subexponential and exponential average-case complexities, depending on the growth of the probability p with respect to the number n of nodes. (c) 2023 Elsevier B.V. All rights reserved.
Exact Algorithms and Lowerbounds for Multiagent Path Finding: Power of Treelike Topology
Authors
Year
2024
Published
Proceedings of the 38th AAAI Conference on Artificial Intelligence. Menlo Park: AAAI Press, 2024. p. 17380-17388. ISSN 2159-5399.
Type
Proceedings paper
Departments
Annotation
In the Multiagent Path Finding (MAPF for short) problem, we focus on efficiently finding non-colliding paths for a set of k agents on a given graph G, where each agent seeks a path from its source vertex to a target. An important measure of the quality of the solution is the length of the proposed schedule l, that is, the length of a longest path (including the waiting time). In this work, we propose a systematic study under the parameterized complexity framework. The hardness results we provide align with many heuristics used for this problem, whose running time could potentially be improved based on our Fixed-Parameter Tractability (FPT) results. We show that MAPF is W[1]-hard with respect to k (even if k is combined with the maximum degree of the input graph). The problem remains NP-hard in planar graphs even if the maximum degree and the makespan l are fixed constants. On the positive side, we show an FPT algorithm for k+l. As we continue, the structure of G comes into play. We give an FPT algorithm for parameter k plus the diameter of the graph G. The MAPF problem is W[1]-hard for cliquewidth of G plus l while it is FPT for treewidth of G plus l.