G. Stacey Staples

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An innovative minimal paths algorithm based on operator calculus in graded semigroup algebras is described. Classical approaches to routing problems invariably require construction of trees and the use of heuristics to prevent combinatorial explosion. The operator calculus approach presented herein, however, allows such explicit tree constructions to be(More)
A number of combinatorial problems are treated using properties of abelian nilpotentand idempotent-generated subalgebras of Clifford algebras. For example, the problem of deciding whether or not a graph contains a Hamiltonian cycle is known to be NP-complete. By considering entries of Λ, where Λ is an appropriate nilpotent adjacency matrix, the k-cycles in(More)
While powers of the adjacency matrix of a finite graph reveal information about walks on the graph, they fail to distinguish closed walks from cycles. Using elements of an appropriate commutative, nilpotentgenerated algebra, a “new” adjacency matrix can be associated with a random graph on n vertices and |E| edges of nonzero probability. Letting Xk denote(More)
Wireless sensor networks (WSN) are inherently multi - constrained. They need to preserve energy while offering reliable and timely data reporting for a non-negligible number of scenarios. This is particularly true when a node should decide which forwarder has to be chosen for routing a packet. Nevertheless, solving multi-constrained routing problems is(More)
Questions about a graph’s connected components are answered by studying appropriate powers of a special “adjacency matrix” constructed with entries in a commutative algebra whose generators are idempotent. The approach is then applied to the Erdös-Rényi model of sequences of random graphs. Developed herein is a method of encoding the relevant information(More)
For fixed n > 0, the space of finite graphs on n vertices is canonically associated with an abelian, nilpotent-generated subalgebra of the 2n-particle fermion algebra. Using the generators of the subalgebra, an algebraic probability space of “nilpotent adjacency matrices” associated with finite graphs is defined. Each nilpotent adjacency matrix is a quantum(More)