A message-passing algorithm for counting short cycles in a graph is presented. For bipartite
graphs, which are of particular interest in coding, the algorithm is capable of counting cycles …

Strassen's method is not the asymptotically fastest known matrix multiplication algorithm, but
it is the most widely used for large matrices. Since his manuscript was published, a number …

An innovative minimal paths algorithm based on operator calculus in graded semigroup
algebras is described. Classical approaches to routing problems invariably require …

A number of combinatorial problems are treated using properties of abelian null-square-
generated and idempotent-generated subalgebras of Clifford algebras. For example, the …

The process of searching for a dynamic constrained optimal path has received increasing
attention in traffic planning, evacuation, and personalized or collaborative traffic service. As …

Nilpotent adjacency matrix methods are employed to count k-cycles in simple graphs on n
vertices for any k≤ n. The worst-case time complexity of counting k-cycles in an n-vertex …

Central to the theory of free probability is the notion of summing multiplicative functionals on
the lattice of non-crossing partitions. In this paper, a graph-theoretic perspective of partitions …

Classical approaches to multi-constrained routing problems generally require construction
of trees and the use of heuristics to prevent combinatorial explosion. Introduced here is the …

Classical approaches to routing problems often employ construction of trees and the use of
heuristics to prevent combinatorial explosion. The algebraic approach presented herein …

A random geometric graph is constructed by randomly choosing a set of points in the unit
cube [0, 1] d and connecting two points by an edge if their Euclidean distance is at most …