Topological graph theory. Aperiodicity. Paths and cycles (Graph theory)
The condition ""every cycle has an entry"" first appeared in the literature in Kumjian, Pask, and Raeburn's paper on Cuntz-Krieger algebras of directed graphs, where it was called Condition (L). It provides a necessary condition for simplicity of...
In the Firefighter Problem, a fire starts at a vertex of a graph, and in discrete time units, it spreads from burned vertices to their neighbors, unless they are protected by one of the f firefighters that are deployed every turn. Once burned or...
In large and complex networks such as the Internet and road networks, traffic routing is typically decentralized. Users in the network choose their routes independently to minimize their own delay, leading to complicated and nonintuitive outcomes...
Modern distributed systems scatter sensors, storage, and computation throughout the environment. Ideally these devices communicate and share resources, but there is seldom motivation for a device''s owner to yield control to another user. We...
We present a number of findings concerning groupoid dynamical systems and groupoid crossed products. The primary result is an identification of the spectrum of the groupoid crossed product when the groupoid has continuously varying abelian...
Partially ordered sets and permutations are combinatorial structures having vast applications in theoretical computer science. In this thesis, we study various computational and algorithmic problems related to these structures. The first chapter of...
'Orthogonal modular forms are algebraic modular forms arising from lattices in quadratic spaces. In this thesis, we define orthogonal modular forms, establish their basic properties, and then apply them to a case of ternary quadratic spaces to...
Electronic data processing -- Distributed processing. ; Computer network architectures. ; Programming languages (Electronic computers) -- Semantics. ; Database management.
I tackle the problem of naming and sharing resources across administrative boundaries. Conventional systems manifest the hierarchy of typical administrative structure in the structure of their own mechanism. While natural for communication that...
We associate, to each positive integer n , a Cayley graph to the group PSL(2.Î–[subscript n]). We then consider the isoperimetric numbers of these graphs. In chapter three we determine upper bounds for the isoperimetric number by a detailed...
Robots -- Control systems. ; Robots -- Motion. ; Computer algorithms. ; Electronic data processing -- Distributed processing.
Self-reconfiguring robots are robots composed of many physically connected modules which can change their structural configuration to support multiple functionalities. We claim that self-reconfiguring robots are more versatile, extensible, and...