Related papers: Generating functions partitioning algorithm for co…
We propose the study of computing the Shapley value for a new class of cooperative games that we call budgeted games, and investigate in particular knapsack budgeted games, a version modeled after the classical knapsack problem. In these…
This paper defines a general class of cooperative games for which the nucleolus is efficiently computable. This class includes new members for which the complexity of computing their nucleolus was not previously known. We show that when the…
Probabilistic graphical models have emerged as a powerful modeling tool for several real-world scenarios where one needs to reason under uncertainty. A graphical model's partition function is a central quantity of interest, and its…
In this paper, we consider different constrained partition problems for weighted trees and cactus graphs. We focus on the (l,u)-partition problem, which is the problem of partitioning a weighted graph into connected clusters such that each…
Important decisions are likely made by groups of agents. Thus group decision making is very common in practice. Very transparent group aggregating rules are given by weighted voting, where each agent is assigned a weight. Here a proposal is…
Weighted Timed Games (WTG for short) are the most widely used model to describe controller synthesis problems involving real-time issues. Unfortunately, they are notoriously difficult, and undecidable in general. As a consequence, one-clock…
A simple game $(N,v)$ is given by a set $N$ of $n$ players and a partition of $2^N$ into a set $\mathcal{L}$ of losing coalitions $L$ with value $v(L)=0$ that is closed under taking subsets and a set $\mathcal{W}$ of winning coalitions $W$…
We consider the problem of computing ratings using the results of games played between a set of n players, and show how this problem can be reduced to computing the positive eigenvectors corresponding to the dominant eigenvalues of certain…
We establish the average-case hardness of the algorithmic problem of exact computation of the partition function associated with the Sherrington-Kirkpatrick model of spin glasses with Gaussian couplings and random external field. In…
Generating functions, which are widely used in combinatorics and probability theory, encode function values into the coefficients of a polynomial. In this paper, we explore their use as a tractable probabilistic model, and propose…
Shapley values are great analytical tools in game theory to measure the importance of a player in a game. Due to their axiomatic and desirable properties such as efficiency, they have become popular for feature importance analysis in data…
The number partition problem is a well-known problem, which is one of 21 Karp's NP-complete problems \cite{karp}. The partition function is a boolean function that is equivalent to the number partition problem with number range restricted.…
This note introduces a new class of integer factoring algorithms. Two versions of this method will be described, deterministic and probabilistic. These algorithms are practical, and can factor large classes of balanced integers N = pq, p <…
An M-partition of a positive integer m is a partition with as few parts as possible such that any positive integer less than m has a partition made up of parts taken from that partition of m. This is equivalent to partitioning a weight m so…
The object of this paper is to introduce a new weighted information generating function whose derivative at point 1 gives some well known measures of information. Some properties and particular cases of the proposed generating function have…
Within the domain of game theory, power indexes are defined as functions that quantify the influence of individual participants in collective decision-making processes. Felsenthal [D. Felsenthal. A Well-Behaved Index of a Priori P-Power for…
Understanding the influence of features in machine learning is crucial to interpreting models and selecting the best features for classification. In this work we propose the use of principles from coalitional game theory to reason about…
This paper employs switching-algebraic techniques for the calculation of a fundamental index of voting powers, namely, the total Banzhaf power. This calculation involves two distinct operations: (a) Boolean differencing or differentiation,…
In binary polynomial optimization, the goal is to find a binary point maximizing a given polynomial function. In this paper, we propose a novel way of formulating this general optimization problem, which we call factorized binary polynomial…
In a mean-payoff parity game, one of the two players aims both to achieve a qualitative parity objective and to minimize a quantitative long-term average of payoffs (aka. mean payoff). The game is zero-sum and hence the aim of the other…