Finding Diverse Trees, Paths, and More

Mathematical modeling is a standard approach to solve many real-world problems and diversity of solutions an important issue, emerging in applying obtained from mathematical models problems. Many studies have been devoted finding diverse solutions. Baste et al. (Algorithms 2019, IJCAI 2020) recently initiated the study computing combinatorial perspective fixed-parameter tractability. They considered r that maximize some measures (the minimum or sum pairwise Hamming distances among them) gave tractable algorithms for version several well-known problems, such as Vertex Cover, Feedback Set, d-Hitting Set}, on bounded-treewidth graphs. In this work, we further investigate (fixed-parameter) tractability spanning trees, paths, subgraphs. particular, show that, given graph G integer r, problem trees maximizing them can be solved polynomial time. To best authors' knowledge, first polynomial-time solvable case unbounded size.