How Do We Assess How Agentic We Are? A Literature Review of Existing Instruments to Evaluate and Measure Individuals' Agency

Social Indicators Research - The importance and centrality of the construct of agency is wellknown amongst social scientists. Yet, there is still little agreement on how this construct should be...     

Minimum entropy coloring

We study an information-theoretic variant of the graph coloring problem in which the objective function to minimize is the entropy of the coloring. The minimum entropy of a coloring is called the chromatic entropy and was shown by Alon and Orlitsky (IEEE Trans. Inform. Theory 42(5):1329–1339, 1996) to play a fundamental role in the problem of coding with side information. In this paper, we consider the minimum entropy coloring problem from a computational point of view. We first prove that this problem is NP-hard on interval graphs. We then show that, for every constant ε>0, it is NP-hard to find a coloring whose entropy is within (1−ε)log n of the chromatic entropy, where n is the number of vertices of the graph. A simple polynomial case is also identified. It is known that graph entropy is a lower bound for the chromatic entropy. We prove that this bound can be arbitrarily bad, even for chordal graphs. Finally, we consider the minimum number of colors required to achieve minimum entropy and prove a Brooks-type theorem. S. Fiorini acknowledges the support from the Fonds National de la Recherche Scientifique and GERAD-HEC Montréal. G. Joret is a F.R.S.-FNRS Research Fellow.     

A closest vector problem arising in radiation therapy planning

In this paper we consider the following closest vector problem. We are given a set of 0–1 vectors, the generators, an integer vector, the target vector, and a nonnegative integer C. Among all vectors that can be written as nonnegative integer linear combinations of the generators, we seek a vector whose ℓ _∞-distance to the target vector does not exceed C, and whose ℓ ₁-distance to the target vector is minimum.     

The Stackelberg minimum spanning tree game on planar and bounded-treewidth graphs

The Stackelberg Minimum Spanning Tree Game is a two-level combinatorial pricing problem played on a graph representing a network. Its edges are colored either red or blue, and the red edges have a given fixed cost, representing the competitor’s prices. The first player chooses an assignment of prices to the blue edges, and the second player then buys the cheapest spanning tree, using any combination of red and blue edges. The goal of the first player is to maximize the total price of purchased blue edges. We study this problem in the cases of planar and bounded-treewidth graphs. We show that the problem is NP-hard on planar graphs but can be solved in polynomial time on graphs of bounded treewidth.