Graph theory and algorithms

Algorithms in Graph Theory

Graph Theory Based Routing Algorithms

Algorithms, Graph Theory, and Linear Equations in Laplacian Matrices

The Laplacian matrices of graphs are fundamental. In addition to facilitating the application of linear algebra to graph theory, they arise in many practical problems. In this talk we survey recent progress on the design of provably fast algorithms for solving linear equations in the Laplacian matrices of graphs. These algorithms motivate and rely upon fascinating primitives in graph theory, in...

Theory and Techniques for Synthesizing a Family of Graph Algorithms

Although Breadth-First Search (BFS) has several advantages over Depth-First Search (DFS) its prohibitive space requirements have meant that algorithm designers often pass it over in favor of DFS. To address this shortcoming, we introduce a theory of Efficient BFS (EBFS) along with a simple recursive program schema for carrying out the search. The theory is based on dominance relations, a long s...

Searching the Nodes of a Graph: Theory and Algorithms

One or more searchers must capture an invisible evader hiding in the nodes of a graph. We study this version of the graph search problem under additional restrictions, such as monotonicity and connectedness. We emphasize that we study node search, i.e., the capture of a node-located evader; this problem has so far received much less attention than edge search, i.e., the capture of an edge-locat...