December 2025
Intermediate to advanced
576 pages
14h 22m
English
book
Graph Theory for Computer Science
by Manikandan Rajagopal, Ramkumar Sivasakthivel, Joseph Varghese Kureethara, Niranjanamurthy M., Biswadip Basu Mallik
Content preview from Graph Theory for Computer Science
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1A Comprehensive Study on Pathfinding in Dynamic Graphs Using Automaton and Two-Way Depth-First Search
Ajayaditya L.1 and Anitha N.2*
1Department of Mechatronics, Kumaraguru College of Technology, Coimbatore, India
2Department of Mathematics, Kumaraguru College of Technology, Coimbatore, India
Abstract
Efficient pathfinding in time-varying directed acyclic graphs is crucial for numerous applications, necessitating incremental updates and maintenance of connectivity. This paper presents a formal automata-theoretic approach combining graph automata, graph transducers, and two-way search techniques. Graph automata model the dynamic acyclic graph evolution, transitioning between configurations. Graph transducers apply transformation rules to handle dynamic changes such as node and edge additions, removals, and property modifications. Two-way breadth-first and depth-first searches augmented with graph walking automata explore the dynamic acyclic graphs, computing potential paths and reconnecting affected routes. Incremental path update algorithms identify impacted regions, apply transducer rules, and reconnect paths via localized two-way searches. Path optimization strategies further enhance efficiency. Comprehensive mathematical formulations, algorithms, and complexity analyses demonstrate the approach’s rigor and applicability to resilient pathfinding in evolving dynamic acyclic graphs.
Keywords: Directed acyclic graphs (DAGs), dynamic graphs, incremental pathfinding, graph automata, ...
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