Minimum Scan Cover and Variants: Theory and Experiments

We consider a spectrum of geometric optimization problems motivated by contexts such as satellite communication and astrophysics. In the problem Minimum Scan Cover with Angular Costs , we are given graph G that is embedded in Euclidean space. The edges need to be scanned, i.e., probed from both their vertices. To scan edge, two vertices face each other; changing heading vertex incurs some cost terms energy or rotation time proportional corresponding angle. Our goal compute schedules minimize following objective functions: (i) Makespan (MSC-MS), this until all scanned; (ii) Total Energy (MSC-TE), sum angles; (iii) Bottleneck (MSC-BE), maximum total angle at one vertex. Previous theoretical work on MSC-MS revealed close connection coloring cut cover problem, leading hardness approximability results. article, present polynomial-time algorithms for one-dimensional (1D) instances MSC-TE MSC-BE but NP-hardness proofs bipartite 2D instances. For graphs 2D, also give 2-approximation MSC-BE. Most importantly, provide comprehensive study practical methods three problems. compare different mixed-integer programming constraint approaches show how provably optimal solutions up 300 edges. Additionally, performance meta-heuristics even larger