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

12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess