Učinkovitost algoritmov za iskanje največje neodvisne množice vozlišč v grafih - Škerlep, Matej (Matrika, 2021)
Finding the maximum independent vertex set is an intriguing graph theoretical problem that is extremely useful in determining sequences in deoxyribonucleic acids. In this paper, the problem is defined as an integer linear program and contrasted to the relaxation of it. The assessments of the integer linear program, its relaxation, and the algorithm for local search in a graph are based on the output set's cardinality and the run-time analyses. Experiments are performed on random graphs with up to 100 vertices, which have a different probability of an edge connecting two arbitrary vertices. For analysis of the algorithm's run-time, the number of vertices is increased to 2401. Finally, tests are carried out on the Petersen graph and n-dimensional hypercubes for 1 ?$≤$? n ?$≤$? 12. On the latter, even the relaxation of the integer linear program successfully finds the maximum independent set, which enabled making insightful comparisons of run-time.
Keywords: algorithms; algoritmi za iskanje vozlišč; graph theory; hiperkocke; hypercubes; Petersen graph; Petersenov graf; teorija grafov; vertices; vozlišča