Name
Abstract | ||
|---|---|---|
We consider the problem of deciding whether a given directed graph can be vertex partitioned into two acyclic subgraphs. Applications of this problem include testing rationality of collective consumption behavior, a subject in microeconomics. We prove that the problem is NP-complete even for oriented graphs and argue that the existence of a constant-factor approximation algorithm is unlikely for an optimization version that maximizes the number of vertices that can be colored using two colors while avoiding monochromatic cycles. We present three exact algorithms---namely, an integer-programming algorithm based on cycle identification, a backtracking algorithm, and a branch-and-check algorithm. We compare these three algorithms both on real-life instances and on randomly generated graphs. We find that for the latter set of graphs, every algorithm solves instances of considerable size within a few seconds; however, the CPU time of the integer-programming algorithm increases with the number of vertices in the graph more clearly than the CPU time of the two other procedures. For real-life instances, the integer-programming algorithm solves the largest instance in about a half hour, whereas the branch-and-check algorithm takes approximately 10 minutes and the backtracking algorithm less than 5 minutes. Finally, for every algorithm, we also study empirically the transition from a high to a low probability of a YES answer as a function of the number of arcs divided by the number of vertices. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1287/ijoc.1110.0466 | INFORMS Journal on Computing |
Keywords | Field | DocType |
yes answer,backtracking algorithm,real-life instance,integer-programming algorithm,coloring graphs,integer-programming algorithm increase,cpu time,oriented graph,constant-factor approximation algorithm,monochromatic cycles,branch-and-check algorithm,exact algorithm,acyclic graph,np complete,bipartite graph,phase transition,directed graph | Discrete mathematics,Mathematical optimization,Combinatorics,Chordal graph,Cycle graph,Matching (graph theory),Hopcroft–Karp algorithm,Independent set,Suurballe's algorithm,Greedy coloring,Mathematics,Graph coloring | Journal |
Volume | Issue | ISSN |
24 | 3 | 1091-9856 |
Citations | PageRank | References |
4 | 0.62 | 20 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Fabrice Talla Nobibon | 1 | 100 | 9.86 |
| Cor A. J. Hurkens | 2 | 430 | 30.75 |
| Roel Leus | 3 | 663 | 43.29 |
| Frits C. R. Spieksma | 4 | 591 | 58.84 |