On Voting Caterpillars: Approximating Maximum Degree in a Tournament by Binary Trees
نویسندگان
چکیده
Voting trees describe an iterative procedure for selecting a single vertex from a tournament. It has long been known that there is no voting tree that always singles out a vertex with maximum degree. In this paper, we study the power of voting trees in approximating the maximum degree. We give upper and lower bounds on the worst-case ratio between the degree of the vertex chosen by a tree and the maximum degree, both for the deterministic model concerned with a single fixed tree, and for randomizations over arbitrary sets of trees. Our main positive result is a randomization over surjective trees of polynomial size that provides an approximation ratio of at least 1/2. The proof is based on a connection between a randomization over caterpillar trees and a rapidly mixing Markov chain.
منابع مشابه
Computing with voting trees
The classical paradox of social choice theory asserts that there is no fair way to deterministically select a winner in an election among more than two candidates; the only definite collective preferences are between individual pairs of candidates. Combinatorially, one may summarize this information with a graph-theoretic tournament on n vertices (one per candidate), placing an edge from u to v...
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