Related papers: Approximate Core Allocations for Edge Cover Games
The classic paper of Shapley and Shubik \cite{Shapley1971assignment} characterized the core of the assignment game using ideas from matching theory and LP-duality theory and their highly non-trivial interplay. Whereas the core of this game…
LP-duality theory has played a central role in the study of cores of games, right from the early days of this notion to the present time. The classic paper of Shapley and Shubik \cite{Shapley1971assignment} introduced the "right" way of…
We consider a natural generalization of the Partial Vertex Cover problem. Here an instance consists of a graph G = (V,E), a positive cost function c: V-> Z^{+}, a partition $P_1,..., P_r$ of the edge set $E$, and a parameter $k_i$ for each…
This paper proposes a novel algorithm to approximate the core of transferable utility (TU) cooperative games via linear programming. Given the computational hardness of determining the full core, our approach provides a tractable…
The matching game is a cooperative game where the value of every coalition is the maximum revenue of players in the coalition can make by forming pairwise disjoint partners. The multiple partners matching game generalizes the matching game…
Eternal Vertex Cover problem is a dynamic variant of the vertex cover problem. We have a two player game in which guards are placed on some vertices of a graph. In every move, one player (the attacker) attacks an edge. In response to the…
The arboricity of a graph is the minimum number of forests required to cover all its edges. In this paper, we examine arboricity from a game-theoretic perspective and investigate cost-sharing in the minimum forest cover problem. We…
We introduce Shortest Connection Game, a two-player game played on a directed graph with edge costs. Given two designated vertices in which they start, the players take turns in choosing edges emanating from the vertex they are currently…
In this paper, we study two generalizations of Vertex Cover and Edge Cover, namely Colorful Vertex Cover and Colorful Edge Cover. In the Colorful Vertex Cover problem, given an $n$-vertex edge-colored graph $G$ with colors from $\{1,…
The reload cost refers to the cost that occurs along a path on an edge-colored graph when it traverses an internal vertex between two edges of different colors. Galbiati et al.[1] introduced the Minimum Reload Cost Cycle Cover problem,…
We present a general framework to model strategic aspects and stable and fair resource allocations in networks via variants and generalizations of path coalitional games. In these games, a coalition of edges or vertices is successful if it…
The vertex cover problem is a famous combinatorial problem, and its complexity has been heavily studied. While a 2-approximation can be trivially obtained for it, researchers have not been able to approximate it better than 2-\textit{o}(1).…
The core is a central solution concept in cooperative game theory, defined as the set of feasible allocations or payments such that no subset of agents has incentive to break away and form their own subgroup or coalition. However, it has…
We examine cooperative games where the viability of a coalition is determined by whether or not its members have the ability to communicate amongst themselves independently of non-members. This necessary condition for viability was proposed…
We present a new class of vertex cover and set cover games. The price of anarchy bounds match the best known constant factor approximation guarantees for the centralized optimization problems for linear and also for submodular costs -- in…
Given a graph $G=(V,E)$ with costs on its edges, the minimum-cost edge cover problem consists of finding a subset of $E$ covering all vertices in $V$ at minimum cost. If $G$ is bipartite, this problem can be solved in time $O(|V|^3)$ via a…
Cooperative games with nonempty core are called balanced, and the set of balanced games is a polyhedron. Given a game with empty core, we look for the closest balanced game, in the sense of the (weighted) Euclidean distance, i.e., the…
We investigate flow games featuring both private arcs owned by individual players and public arcs accessible cost-free to all coalitions. We explore two solution concepts within this framework: the approximate core and the nucleon. The…
The vertex cover problem is a fundamental and widely studied combinatorial optimization problem. It is known that its standard linear programming relaxation is integral for bipartite graphs and half-integral for general graphs. As a…
A cycle cover of a graph is a set of cycles such that every vertex is part of exactly one cycle. An L-cycle cover is a cycle cover in which the length of every cycle is in the set L. The weight of a cycle cover of an edge-weighted graph is…