The Sum-over-Forests Density Index: Identifying Dense Regions in a Graph.

This work introduces a novel nonparametric density index defined on graphs, the Sum-over-Forests (SoF) density index. It is based on a clear and intuitive idea: high-density regions in a graph are characterized by the fact that they contain a large amount of low-cost trees with high outdegrees while low-density regions contain few ones. Therefore, a Boltzmann probability distribution on the countable set of forests in the graph is defined so that large (high-cost) forests occur with a low probability while short (low-cost) forests occur with a high probability.

Rminimax: An Optimally Randomized MINIMAX Algorithm.

This paper proposes a simple extension of the celebrated MINIMAX algorithm used in zero-sum two-player games, called Rminimax. The Rminimax algorithm allows controlling the strength of an artificial rival by randomizing its strategy in an optimal way. In particular, the randomized shortest-path framework is applied for biasing the artificial intelligence (AI) adversary toward worse or better solutions, therefore controlling its strength.