# Algoraph but in C++

## Faculty Mentor(s)

Dr. Charles Cusack, Computer Science

Poster

4-22-2022

## Abstract

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.