Various least core concepts including the classical least core of cooperative games are discussed. By a reduction from minimum cover problems, we prove that computing an element in these least cores is in general NP-hard for minimum cost spanning tree games. As a consequence, computing the...

The lexicographic kernel of a game lexicographically maximizes the surplusses s ij (rather than the excesses as would the nucleolus) and is contained in both the least core and the kernel. We show that an element in the lexicographic kernel can be computed efficiently, provided we can...

The lexicographic kernel of a game lexicographically maximizes the surplusses s <Subscript> ij </Subscript> (rather than the excesses as would the nucleolus) and is contained in both the least core and the kernel. We show that an element in the lexicographic kernel can be computed efficiently, provided we can...</subscript>

We prove that computing the nucleolus of minimum cost spanning tree games is in general NP-hard. The proof uses a reduction from minimum cover problems.

We consider classes of cooperative games. We show that we can efficiently compute an allocation in the intersection of the prekernel and the least core of the game if we can efficiently compute the minimum excess for any given allocation. In the case where the prekernel of the game contains...

Let $N=\{ 1,...,n\} $ be a finite set of players and $K_{N}$ the complete graph on the node set $N\cup \{ 0\} $. Assume that the edges of $K_{N}$ have nonnegative weights and associate with each coalition $S\subseteq N$ of players as cost $c(S)$ the weight of a minimal spanning tree on the node...

The Dreyfus–Wagner algorithm is a well-known dynamic programming method for computing minimum Steiner trees in general weighted graphs in time O * (3 k ), where k is the number of terminal nodes to be connected. We improve its running time to O * (2.684 k ) by showing that the optimum Steiner...

The stable roommates problem with payments has as input a graph G(E,V) with an edge weighting w:E_ùR+ and the problem is to find a stable solution. A solution is a matching M with a vector p.RV that satisfies pu+pv=w(uv) for all uv.M and pu=0 for all u unmatched in M. A solution is stable if it...