Faculty Mentor(s)

Dr. Charles Cusack, Hope College

Document Type


Publication Date



This work was supported by the National Science Foundation Research Experience for Undergraduates Program grant No. 0851293.


Graph Games is a suite of online casual games that make use of human computation to help solve several NP-complete graph problems. These problems are very difficult for computers to solve efficiently because they rapidly become computationally infeasible as their size increases. However, humans possess intelligent decision-making abilities that computers do not, so they can solve these problems more resourcefully than computers.

Graph Games seeks to harness these abilities to increase the body of knowledge about solving NP-complete problem by presenting problems in the form of puzzle-like games. Graph Games currently consists of three families of games, each being comprised of several types of puzzles based on related problems. Pebble It helps solve graph pebbling problems. Graph pebbling problems involve the placement and/or movement of resources (called pebbles) under certain constraints. Power Graph puzzles are based on the vertex cover and dominating set problems. These problems require finding minimal subsets of the vertices of the graph that are adjacent to all edges or vertices in the graph. In these puzzles, players must activate as few power stations as possible to provide energy to an entire power grid. Finally, Portal Lord is based on the problem of graph bandwidth. In this game, players must build stabilizers on portals and assign addresses to them in such a way that the addresses of adjacent nodes are as close together as possible. We believe that by using this platform, ordinary gamers will contribute valuable insights to researchers working to solve NP-complete problems.