Problem
Research questions and friction points this paper is trying to address.
binary k-center
delegated voting
computational social choice
approval voting
string covering
Binary $k$-Center under a Hard Threshold with Applications to Delegated Voting
🤖 AI Summary
This study addresses the $k$-center coverage problem for binary strings with missing values under hard threshold constraints, aiming to provide theoretical foundations for representative generation mechanisms in liquid democracy within computational social choice. Methodologically, by leveraging combinatorial optimization and computational complexity theory, this work establishes a complete complexity landscape for scenarios involving missing values and extends hardness results from settings without missing values to arbitrary numbers of centers and broad threshold ranges. The primary contribution lies in precisely delineating the computational complexity boundaries of this problem, leaving only a few narrow threshold intervals unresolved. Consequently, this research lays a rigorous theoretical groundwork for designing efficient representative selection mechanisms in multi-issue approval voting.
📝 Abstract
We study the problem of covering binary strings of the same length, possibly with missing entries, by a fixed number of center strings, such that each input string is within a given relative distance of the closest center. The problem has applications in binary $k$-center clustering and bioinformatics, but our main motivation comes from computational social choice. In the setting of multi-issue approval voting, we consider an algorithmic question that precedes any election: how should representatives be designed so that as many voters as possible are willing to delegate? We study the problem in two dimensions, namely the number of centers and the agreement threshold, parameters that are application-specific, and provide a complete picture of its computational complexity when entries may be missing. For the special case without missing entries, we extend our hardness results to any number of centers and large values of threshold, leaving a narrow range of thresholds unresolved.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Binary k-Center
Delegated Voting
Computational Complexity
Approval Voting
Missing Entries
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