Chaotic Traversal (CHAT): Very Large Graphs Traversal Using Chaotic Dynamics

Abstract

Graph Traversal algorithms can find their applications in various fields such as routing problems, natural language processing or even database querying. The exploration can be considered as a first stepping stone into knowledge extraction from the graph which is now a popular topic. Classical solutions such as Breadth First Search (BFS) and Depth First Search (DFS) require huge amounts of memory for exploring very large graphs. In this research, we present a novel memoryless graph traversal algorithm, Chaotic Traversal (CHAT) which integrates chaotic dynamics to traverse large unknown graphs via the Lozi map and the Rössler system. To compare various dynamics effects on our algorithm, we present an original way to perform the exploration of a parameter space using a bifurcation diagram with respect to the topological structure of attractors. The resulting algorithm is an efficient and nonresource demanding algorithm, and is therefore very suitable for partial traversal of very large and/or unknown environment graphs. CHAT performance using Lozi map is proven superior than the, commonly known, Random Walk, in terms of number of nodes visited (coverage percentage) and computation time where the environment is unknown and memory usage is restricted.

Bayesian optimisation to select Rössler system parameters used in Chaotic Ant Colony Optimisation for Coverage

“…The values of this discrete map are used in an algorithm to generate a Chaotic Pseudo Random Numbers (CPRNG) in order to replace the Random Number Generator (RNG) used in a PSO algorithm. We recently tune the Lozi map parameter values, as well as the Rössler system parameters to determine the best parameter values for a given optimisation problem: the graph traversal problem [13].…”

“…The two previous articles [11,13] compare all the results for parameters in a given range of values; this approach is time consuming and can be repetitive since the dynamics are the same for various parameter values (see [14] for details on the chaotic dynamics of the Rössler system). To obtain the parameter values of a chaotic system, Senkerik et al [15] propose to use a combination of evolutionary algorithms: Differential Evolution (DE) and Self-Organizing Migrating Algorithm (SOMA).…”

Shimizu–Morioka's chaos synchronization: An efficacy analysis of active control and backstepping methods

“…Since Lorenz discovered the first chaotic systems with a strange chaotic attractor [23], other chaotic systems began to be studied, namely, the Henon map, Rössler chaotic attractor [24], Chua's chaotic attractor in double scroll [25], Chen chaotic attractor [26], and Lü chaotic attractor. Shimizu and Morioka [27] introduced continuous-time chaotic systems, becoming one of the significant chaotic systems.…”