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We propose models for lobbying in a probabilistic environment, in which an actor (called The Lobby) seeks to influence voters preferences of voting for or against multiple issues when the voters preferences are represented in terms of probabilities. In particular, we provide two evaluation criteria and two bribery methods to formally describe these models, and we consider the resulting forms of lobbying with and without issue weighting. We provide a formal analysis for these problems of lobbying in a stochastic environment, and determine their classical and parameterized complexity depending on the given bribery/evaluation criteria and on various natural parameterizations. Specifically, we show that some of these problems can be solved in polynomial time, some are NP-complete but fixed-parameter tractable, and some are W[2]-complete. Finally, we provide approximability and inapproximability results for these problems and several variants.
Rummikub is a tile-based game in which each player starts with a hand of $14$ tiles. A tile has a value and a suit. The players form sets consisting of tiles with the same suit and consecutive values (runs) or tiles with the same value and different
We study the complexity of approximating the vertex expansion of graphs $G = (V,E)$, defined as [ Phi^V := min_{S subset V} n cdot frac{|N(S)|}{|S| |V backslash S|}. ] We give a simple polynomial-time algorithm for finding a subset with vertex expa
In two papers, Burgisser and Ikenmeyer (STOC 2011, STOC 2013) used an adaption of the geometric complexity theory (GCT) approach by Mulmuley and Sohoni (Siam J Comput 2001, 2008) to prove lower bounds on the border rank of the matrix multiplication t
The method of partial derivatives is one of the most successful lower bound methods for arithmetic circuits. It uses as a complexity measure the dimension of the span of the partial derivatives of a polynomial. In this paper, we consider this complex
Detecting and eliminating logic hazards in Boolean circuits is a fundamental problem in logic circuit design. We show that there is no $O(3^{(1-epsilon)n} text{poly}(s))$ time algorithm, for any $epsilon > 0$, that detects logic hazards in Boolean ci