Influence of the tie-break rule on the end-vertex problem

International audienceEnd-vertices of a given graph search may have some nice properties, as for example it is well known that the last vertex of Lexicographic Breadth First Search (LBFS) in a chordal graph is simplicial, see Rose, Tarjan and Lueker 1976. Therefore it is interesting to consider if these vertices can be recognized in polynomial time or not, as first studied in Corneil, Köhler and Lanlignel 2010. A graph search is a mechanism for systematically visiting the vertices of a graph. At each step of a graph search, the key point is the choice of the next vertex to be explored. Graph searches only differ by this selection mechanism during which a tie-break rule is used. In this paper we study how the choice of the tie-break in case of equality during the search, for a given graph search including the classic ones such as BFS and DFS, can determine the complexity of the end-vertex problem. In particular we prove a counterintuitive NP-completeness result for Breadth First Search solving a problem raised in Corneil, Köhler and Lanlignel 2010

Manipulation and Control Complexity of Schulze Voting

Schulze voting is a recently introduced voting system enjoying unusual popularity and a high degree of real-world use, with users including the Wikimedia foundation, several branches of the Pirate Party, and MTV. It is a Condorcet voting system that determines the winners of an election using information about paths in a graph representation of the election. We resolve the complexity of many electoral control cases for Schulze voting. We find that it falls short of the best known voting systems in terms of control resistance, demonstrating vulnerabilities of concern to some prospective users of the system

On coalitional manipulation for multiwinner elections: shortlisting

Shortlisting of candidates—selecting a group of “best” candidates—is a special case of multiwinner elections. We provide the first in-depth study of the computational complexity of strategic voting for shortlisting based on the perhaps most basic voting rule in this scenario, -Bloc (every voter approves candidates). In particular, we investigate the influence of several different group evaluation functions (e.g., egalitarian versus utilitarian) and tie-breaking mechanisms modeling pessimistic and optimistic manipulators. Among other things, we conclude that in an egalitarian setting strategic voting may indeed be computationally intractable regardless of the tie-breaking rule. Altogether, we provide a fairly comprehensive picture of the computational complexity landscape of this scenario.Deutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/501100001659Deutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/501100001659Humboldt-Universität zu Berlin (1034)Peer Reviewe

Rank Aggregation Using Scoring Rules

To aggregate rankings into a social ranking, one can use scoring systems such as Plurality, Veto, and Borda. We distinguish three types of methods: ranking by score, ranking by repeatedly choosing a winner that we delete and rank at the top, and ranking by repeatedly choosing a loser that we delete and rank at the bottom. The latter method captures the frequently studied voting rules Single Transferable Vote (aka Instant Runoff Voting), Coombs, and Baldwin. In an experimental analysis, we show that the three types of methods produce different rankings in practice. We also provide evidence that sequentially selecting winners is most suitable to detect the "true" ranking of candidates. For different rules in our classes, we then study the (parameterized) computational complexity of deciding in which positions a given candidate can appear in the chosen ranking. As part of our analysis, we also consider the Winner Determination problem for STV, Coombs, and Baldwin and determine their complexity when there are few voters or candidates.Comment: 47 pages including appendi

A superior edge preserving filter with a systematic analysis

A new, adaptive, edge preserving filter for use in image processing is presented. It had superior performance when compared to other filters. Termed the contiguous K-average, it aggregates pixels by examining all pixels contiguous to an existing cluster and adding the pixel closest to the mean of the existing cluster. The process is iterated until K pixels were accumulated. Rather than simply compare the visual results of processing with this operator to other filters, some approaches were developed which allow quantitative evaluation of how well and filter performs. Particular attention is given to the standard deviation of noise within a feature and the stability of imagery under iterative processing. Demonstrations illustrate the performance of several filters to discriminate against noise and retain edges, the effect of filtering as a preprocessing step, and the utility of the contiguous K-average filter when used with remote sensing data

Failure Localization in Power Systems via Tree Partitions

Cascading failures in power systems propagate non-locally, making the control and mitigation of outages extremely hard. In this work, we use the emerging concept of the tree partition of transmission networks to provide an analytical characterization of line failure localizability in transmission systems. Our results rigorously establish the well perceived intuition in power community that failures cannot cross bridges, and reveal a finer-grained concept that encodes more precise information on failure propagations within tree-partition regions. Specifically, when a non-bridge line is tripped, the impact of this failure only propagates within well-defined components, which we refer to as cells, of the tree partition defined by the bridges. In contrast, when a bridge line is tripped, the impact of this failure propagates globally across the network, affecting the power flow on all remaining transmission lines. This characterization suggests that it is possible to improve the system robustness by temporarily switching off certain transmission lines, so as to create more, smaller components in the tree partition; thus spatially localizing line failures and making the grid less vulnerable to large-scale outages. We illustrate this approach using the IEEE 118-bus test system and demonstrate that switching off a negligible portion of transmission lines allows the impact of line failures to be significantly more localized without substantial changes in line congestion