Faculty Mentor(s)

Dr. Charles Cusack, Computer Science

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Given a configuration of “pebbles” on a graph G, a pebbling move removes two pebbles from a source vertex and one pebble is added to an adjacent vertex. A vertex is reachable if there is a sequence of pebbling moves that places one pebble on that vertex; a graph is solvable if every vertex is reachable. The pebbling number of graph G is the smallest integer π(G), such that any configuration that uses π(G) pebbles is solvable. A graph satisfies the two-pebbling property if for any configuration of more than 2π(G) - q pebbles, where q is the number of vertices in G with at least one pebble, two pebbles can be moved to any vertex. Through heuristics and algorithms, Algoraph is a program that allows a user to run multiple permutations of pebbles on a graph and determine the reachability, solvability, and satisfaction of the two-pebbling property. Algoraph was originally coded in Java by Dr. Cusack and previous research students and was translated into C++ by Adam James Czeranko and Andres Solorzano. Through proper data management and parallelization of code, the team developed a new, more efficient version of Algoraph.


This research was supported by the Department of Computer Science at Hope College and the Dershem Computer Science Summer Research Fund.

Title on poster differs from abstract booklet. Poster title: Algoraph but in C/C++