Clustering, Randomness, and Regularity: Spatial Distributions and Human Performance on the Traveling Salesperson Problem and Minimum Spanning Tree Problem

We investigated human performance on the Euclidean Traveling Salesperson Problem (TSP) and Euclidean Minimum Spanning Tree Problem (MST-P) in regards to a factor that has previously received little attention within the literature: the spatial distributions of TSP and MST-P stimuli. First, we describe a method for quantifying the relative degree of clustering, randomness or regularity within point distributions. We then review evidence suggesting this factor might influence human performance on the two problem types. Following this we report an experiment in which the participants were asked to solve TSP and MST-P test stimuli that had been generated to be either highly clustered, random, or highly regular. The results indicate that for both the TSP and MST-P the participants tended to produce better quality solutions when the stimuli were highly clustered compared to random, and similarly, better quality solutions for random compared to highly regular stimuli. It is suggested that these results provide support for the ideas that human solvers attend to salient clusters of nodes when solving these problems, and that a similar process (or series of processes) may underlie human performance on these two tasks

The Perceptual Organization of Point Constellations

In this paper we present observers with point patterns based on 30 major star constellations and ask them to connect the points to show the structure they perceive. The resulting empirical structures had a high inter-rater reliability and a high degree of overlap with constellation structures recorded in star atlases, suggesting that the perception of structure in point patterns is largely invariant across individuals. Further, we demonstrate that the empirical structures correspond closely with the structures developed in the field of relational geometry. We discuss the results of the experiment in light of previous findings and suggest a number of potential approaches to formally modeling human performance on clustering tasks

The Perceptual Organization of Point Constellations.

Abstract In this paper we present observers with point patterns based on 30 major star constellations and ask them to connect the points to show the structure they perceive. The resulting empirical structures had a high inter-rater reliability and a high degree of overlap with constellation structures recorded in star atlases, suggesting that the perception of structure in point patterns is largely invariant across individuals. Further, we demonstrate that the empirical structures correspond closely with the structures developed in the field of relational geometry. We discuss the results of the experiment in light of previous findings and suggest a number of potential approaches to formally modeling human performance on clustering tasks