Martin Lackner

Computational aspects of nearly single-peaked electorates

Manipulation, bribery, and control are well-studied ways of changing the outcome of an election. Many voting systems are, in the general case, computationally resistant to some of these manipulative actions. However when restricted to single-peaked electorates, these systems suddenly become easy to manipulate. Recently, Faliszewski, Hemaspaandra, and Hemaspaandra (2011b) studied the complexity of dishonest behavior in nearly single-peaked electorates. These are electorates that are not single-peaked but close to it according to some distance measure. In this paper we introduce several new distance measures regarding single-peakedness. We prove that determining whether a given profile is nearly single-peaked is NP-complete in many cases. For one case we present a polynomial-time algorithm. Furthermore, we explore the relations between several notions of nearly single-peakedness.

A Fast Algorithm for Permutation Pattern Matching Based on Alternating Runs

The NP-complete Permutation Pattern Matching problem asks whether a k-permutation P is contained in a n-permutation T as a pattern. This is the case if there exists an order-preserving embedding of P into T. In this paper, we present a fixed-parameter algorithm solving this problem with a worst-case runtime of

Consistent Approval-Based Multi-Winner Rules

{\mathcal O}(1.79^{\mathsf {run}(T)}\cdot n\cdot k)

Manipulation of k-Approval in Nearly Single-Peaked Electorates

O(1.79run(T)·n·k), where

Fixed-parameter algorithms for closed world reasoning

\mathsf {run}(T)

Approval-Based Multi-Winner Rules and Strategic Voting

run(T) denotes the number of alternating runs of T. This algorithm is particularly well-suited for instances where T has few runs, i.e., few ups and downs. Moreover, since