arXiv subjects

Ahmad T. Anaqreh

Publications and source records attributed to Ahmad T. Anaqreh.

2 recordsLinked to original sources

arXiv2023

Exact Methods for the Longest Induced Cycle Problem

The longest induced (or chordless) cycle problem is a graph problem classified as NP-complete and involves the task of determining the largest possible subset of vertices within a graph in such a way that the induced subgraph forms a cycle. Within this paper, we present three integer linear programs specifically formulated to yield optimal solutions for this problem. The branch-and-cut algorithm has been used for two models. To demonstrate the computational efficiency of these methods, we utilize them on a range of real-world graphs as well as random graphs. Additionally, we conduct a comparative analysis against approaches previously proposed in the literature.

cs.DM↗

arXiv2020

Algorithmic upper bounds for graph geodetic number

Graph theoretical problems based on shortest paths are at the core of research due to their theoretical importance and applicability. This paper deals with the geodetic number which is a global measure for simple connected graphs and it belongs to the path covering problems: what is the minimal-cardinality set of vertices, such that all shortest paths between its elements cover every vertex of the graph. Inspired by the exact 0-1 integer linear programming formalism from the recent literature, we propose a new methods to obtain upper bounds for the geodetic number in an algorithmic way. The efficiency of these algorithms are demonstrated on a collection of structurally different graphs.

cs.DS↗