This paper analyzes the computational complexity involved in solving fairness issues on graphs, e.g., in the installation of networks such as water networks or oil pipelines. Based on individual rankings of the edges of a graph, we will show under which conditions solutions, i.e., spanning...

A fair spanning tree of a graph maximizes the minimum satisfaction among individuals given their preferences over the edges of the graph. In this note we answer an open question about the computational complexity of determining fair spanning trees raised in Darmann et al. (2009). It is shown...

In this work we address a game theoretic variant of the Subset Sum problem, in which two decision makers (agents/players) compete for the usage of a common resource represented by a knapsack capacity. Each agent owns a set of integer weighted items and wants to maximize the total weight of its...

This paper considers cost sharing rules for the continuous knapsack problem. We assume a knapsack with a weight constraint to be filled with items of different weights chosen from a set of items. The cost of the knapsack needs to be shared among the individuals who approve or disapprove of...

In this paper we investigate the problem of selecting a committee consisting of k members from a list of m candidates. Each candidate has a certain cost or weight. The choice of the k-committee has to satisfy some budget or weight constraint: the sum of the weights of all committee members must...

We consider the problem of finding a "fair" or "acceptable" spanning tree in an undirected graph when each member of a group of agents proposes a spanning tree. An "acceptable" spanning tree in that respect is a spanning tree which does not differ in more than a given number of edges from each...