Sep 2026· Discrete Mathematics, Algorithms and Applications (DMAA)· 0 citations
TL;DR
This study proposes a hybrid framework that integrates a deep Q-network with a local search algorithm that outperforms baseline algorithms and exhibits strong generalization in the minimum weight k-path vertex cover problem.
Abstract
The minimum weight k-path vertex cover problem is defined on a vertex-weighted graph G, where the objective is to find a vertex subset S such that every path of order k contains at least one vertex in S, while minimizing the total weight of S. For any integer k ≥ 2, this problem is NP-hard on general graphs. In this study, we focused on the case k = 4. We propose a hybrid framework that integrates a deep Q-network with a local search algorithm. Experimental results on randomly generated instances demonstrate that our method outperforms baseline algorithms and exhibits strong generalization.
We study the minimum-weight mixed dominating set problem on threshold graphs. In this problem, vertices and edges have weights, and the goal is to find a mixed set of minimum total weight that dominates every vertex and edge of the graph. We first show that arbitrary weights can be reduced to non-negative weights witho...
For a given geometric graph-convexity on a graph $G$ equipped with a weight function on the vertices with value in $\mathbb{Z}$, the Max Weight Convex Set problem consists in determining the convex set $S$ with maximum weight (sum of the weight of the vertices in $S$). Although the problem is NP-complete in general, it...
Fariza Aklouche, Pierre Bergé, M. Habib· 0 citations
This paper presents an $\frac{11}{6} \approx 1.83$-competitive algorithm for trees in the more general edge arrival model and gives a 1.5-competitive algorithm and provide a matching lower bound.
Júlia Baligács, B. Bosek, Y. Disser et al.· Embedded Systems and Applica...· 1 citation
Suppose that T is a normal spanning tree (depth-first search tree) of a graph G. If e=xy and e′=uv are edges of G, satisfying x≺Tu≺Ty≺Tv, then they are called secant edges of G with respect to T. Suppose that G has no secant edges with respect to T. If T is a path, Ghazal and Al-Mniny proved that the chromatic number i...
This paper develops an exact algorithm based on the Branch and Bound approach for solving PIDS on chordal graphs, which involves identifying the smallest group of vertices in a given network that maximizes influence throughout the network.
Y A Bekhti, M. Lalou, Méziane Aïder et al.· Pesquisa Operacional· 0 citations
A
cubic tree
is a tree with leaves in which every internal vertex has degree exactly 3. Any such tree can be encoded by a
Path‐Length Matrix
(PLM), that is, an integer matrix whose th entry gives the number of edges in the unique path between leaves and in . The convex hull of all PLMs associated with cubic tre...
D. Catanzaro, G. Joret, Brieuc Pierre et al.· Networks· 0 citations
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