Related Experiment Video
Updated: Jun 14, 2026

ExCYT: A Graphical User Interface for Streamlining Analysis of High-Dimensional Cytometry Data
Published on: January 16, 2019
Statistical mechanics of maximal independent sets
Luca Dall'Asta1, Paolo Pin, Abolfazl Ramezanpour
1The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34014 Trieste, Italy.
Abstract:
The graph theoretic concept of maximal independent set arises in several practical problems in computer science as well as in game theory. A maximal independent set is defined by the set of occupied nodes that satisfy some packing and covering constraints. It is known that finding minimum and maximum-density maximal independent sets are hard optimization problems. In this paper, we use cavity method of statistical physics and Monte Carlo simulations to study the corresponding constraint satisfaction problem on random graphs. We obtain the entropy of maximal independent sets within the replica symmetric and one-step replica symmetry breaking frameworks, shedding light on the metric structure of the landscape of solutions and suggesting a class of possible algorithms. This is of particular relevance for the application to the study of strategic interactions in social and economic networks, where maximal independent sets correspond to pure Nash equilibria of a graphical game of public goods allocation.
Related Concept Videos
Introduction to Test of Independence
The test statistic for a test of independence is similar to that of a goodness-of-fit test:
Law of Independent Assortment
Law of Independent Assortment
Probability in Statistics
An example of a simple event is a coin toss. The result of a coin toss is either a head or a tail. Here, head and tail are two simple events. These two simple events make up the sample space. Further, the probability of an event occurring falls within the range of 0 to 1. The probability of an...
Alternative Sets of Equilibrium Equations
One example of such a situation can be observed in a...
Local Maximum and Minimum Values
