Fixed-Parameter Algorithms for Computing Kemeny Scores - Theory and Practice

The central problem in this work is to compute a ranking of a set of elements which is "closest to" a given set of input rankings of the elements. We define "closest to" in an established way as having the minimum sum of Kendall-Tau distances to each input ranking. Unfortunately, the resulting problem Kemeny consensus is NP-hard for instances with n input rankings, n being an even integer greater than three. Nevertheless this problem plays a central role in many rank aggregation problems. It was shown that one can compute the corresponding Kemeny consensus list in f(k) + poly(n) time, being f(k) a computable function in one of the parameters "score of the consensus", "maximum distance between two input rankings", "number of candidates" and "average pairwise Kendall-Tau distance" and poly(n) a polynomial in the input size. This work will demonstrate the practical usefulness of the corresponding algorithms by applying them to randomly generated and several real-world data. Thus, we show that these fixed-parameter algorithms are not only of theoretical interest. In a more theoretical part of this work we will develop an improved fixed-parameter algorithm for the parameter "score of the consensus" having a better upper bound for the running time than previous algorithms.Comment: Studienarbei

Parameterized Algorithmics for Computational Social Choice: Nine Research Challenges

Computational Social Choice is an interdisciplinary research area involving Economics, Political Science, and Social Science on the one side, and Mathematics and Computer Science (including Artificial Intelligence and Multiagent Systems) on the other side. Typical computational problems studied in this field include the vulnerability of voting procedures against attacks, or preference aggregation in multi-agent systems. Parameterized Algorithmics is a subfield of Theoretical Computer Science seeking to exploit meaningful problem-specific parameters in order to identify tractable special cases of in general computationally hard problems. In this paper, we propose nine of our favorite research challenges concerning the parameterized complexity of problems appearing in this context

Unsupervised Graph-based Rank Aggregation for Improved Retrieval

This paper presents a robust and comprehensive graph-based rank aggregation approach, used to combine results of isolated ranker models in retrieval tasks. The method follows an unsupervised scheme, which is independent of how the isolated ranks are formulated. Our approach is able to combine arbitrary models, defined in terms of different ranking criteria, such as those based on textual, image or hybrid content representations. We reformulate the ad-hoc retrieval problem as a document retrieval based on fusion graphs, which we propose as a new unified representation model capable of merging multiple ranks and expressing inter-relationships of retrieval results automatically. By doing so, we claim that the retrieval system can benefit from learning the manifold structure of datasets, thus leading to more effective results. Another contribution is that our graph-based aggregation formulation, unlike existing approaches, allows for encapsulating contextual information encoded from multiple ranks, which can be directly used for ranking, without further computations and post-processing steps over the graphs. Based on the graphs, a novel similarity retrieval score is formulated using an efficient computation of minimum common subgraphs. Finally, another benefit over existing approaches is the absence of hyperparameters. A comprehensive experimental evaluation was conducted considering diverse well-known public datasets, composed of textual, image, and multimodal documents. Performed experiments demonstrate that our method reaches top performance, yielding better effectiveness scores than state-of-the-art baseline methods and promoting large gains over the rankers being fused, thus demonstrating the successful capability of the proposal in representing queries based on a unified graph-based model of rank fusions