arXiv subjects
Publications and source records attributed to Nimrod Talmon.
The goal of this paper is twofold. First and foremost, we aim to experimentally and quantitatively show that the choice of a multiwinner voting rule can play a crucial role on the way minorities are represented. We also test the possibility for some of these rules to achieve proportional representation.
We characterize the class of committee scoring rules that satisfy the fixed-majority criterion. In some sense, the committee scoring rules in this class are multiwinner analogues of the single-winner Plurality rule, which is uniquely characterized as the only single-winner scoring rule that satisfies the simple majority criterion. We define top-$k$-counting committee scoring rules and show that the fixed majority consistent rules are a subclass of the top-$k$-counting rules. We give necessary and sufficient conditions for a top-$k$-counting rule to satisfy the fixed-majority criterion. We find that, for most of the rules in our new class, the complexity of winner determination is high (that is, the problem of computing the winners is NP-hard), but we also show examples of rules with polynomial-time winner determination procedures. For some of the computationally hard rules, we provide either exact FPT algorithms or approximate polynomial-time algorithms.
The NP-hard EFFECTORS problem on directed graphs is motivated by applications in network mining, particularly concerning the analysis of probabilistic information-propagation processes in social networks. In the corresponding model the arcs carry probabilities and there is a probabilistic diffusion process activating nodes by neighboring activated nodes with probabilities as specified by the arcs. The point is to explain a given network activation state as well as possible by using a minimum number of "effector nodes"; these are selected before the activation process starts. We correct, complement, and extend previous work from the data mining community by a more thorough computational complexity analysis of EFFECTORS, identifying both tractable and intractable cases. To this end, we also exploit a parameterization measuring the "degree of randomness" (the number of "really" probabilistic arcs) which might prove useful for analyzing other probabilistic network diffusion problems as well.
Voter control problems model situations such as an external agent trying to affect the result of an election by adding voters, for example by convincing some voters to vote who would otherwise not attend the election. Traditionally, voters are added one at a time, with the goal of making a distinguished alternative win by adding a minimum number of voters. In this paper, we initiate the study of combinatorial variants of control by adding voters: In our setting, when we choose to add a voter~$v$, we also have to add a whole bundle $κ(v)$ of voters associated with $v$. We study the computational complexity of this problem for two of the most basic voting rules, namely the Plurality rule and the Condorcet rule.
The selection problem, where one wishes to locate the $k^{th}$ smallest element in an unsorted array of size $n$, is one of the basic problems studied in computer science. The main focus of this work is designing algorithms for solving the selection problem in the presence of memory faults. These can happen as the result of cosmic rays, alpha particles, or hardware failures. Specifically, the computational model assumed here is a faulty variant of the RAM model (abbreviated as FRAM), which was introduced by Finocchi and Italiano. In this model, the content of memory cells might get corrupted adversarially during the execution, and the algorithm is given an upper bound $δ$ on the number of corruptions that may occur. The main contribution of this work is a deterministic resilient selection algorithm with optimal O(n) worst-case running time. Interestingly, the running time does not depend on the number of faults, and the algorithm does not need to know $δ$. The aforementioned resilient selection algorithm can be used to improve the complexity bounds for resilient $k$-d trees developed by Gieseke, Moruz and Vahrenhold. Specifically, the time complexity for constructing a $k$-d tree is improved from $O(n\log^2 n + δ^2)$ to $O(n \log n)$. Besides the deterministic algorithm, a randomized resilient selection algorithm is developed, which is simpler than the deterministic one, and has $O(n + α)$ expected time complexity and O(1) space complexity (i.e., is in-place). This algorithm is used to develop the first resilient sorting algorithm that is in-place and achieves optimal $O(n\log n + αδ)$ expected running time.