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.
In a round-trip carsharing system, stations must be located in such a way that allow for maximum user coverage with the least walking distance as well as offer certain degrees of flexibility for returning. Therefore, a balance must be stricken between these factors. Providing a satisfactory system can be translated into an optimization problem and belongs to an NP-hard class. In this article, a novel optimization model for the round-trip carsharing fleet placement problem, called Fleet Placement Problem (FPP), is proposed. The optimization in this work is multiobjective and its NP-hard nature is proven. Three different optimization algorithms: PolySCIP (exact method), heuristics, and NSGA-II (metaheuristic) are investigated. This work adopts three real instances for the study, instead of their abstracts where they are most commonly used. They are two instance:, in the city of Luxembourg (smaller and larger) and a much larger instance in the city of Munich. Results from each algorithm are validated and compared with solution from human experts. Superiority of the proposed FPP model over the traditional methods is also demonstrated.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.