The Stackelberg Minimum Spanning Tree Game on Planar and Bounded-Treewidth Graphs
The Stackelberg Minimum Spanning Tree Game is a two-level combinatorial pricing problem introduced at WADS’07. The game is played on a graph, whose edges are colored either red or blue, and where the red edges have a given fixed cost. The first player chooses an assignment of prices to the blue edges, and the second player then buys the cheapest spanning tree, using any combination of red and blue edges. The goal of the first player is to maximize the total price of purchased blue edges. We study this problem in the cases of planar and bounded-treewidth graphs. We show that the problem is NP-hard on planar graphs but can be solved in polynomial time on graphs of bounded treewidth.
KeywordsPlanar Graph Parallel Composition Boundary Vertex Series Composition Short Path Tree
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- [AF93]Abrahamson, K.R., Fellows, M.R.: Finite automata, bounded treewidth, and well-quasiordering. In: Robertson, N., Seymour, P. (eds.) Graph Structure Theory, pp. 539–564 (1993)Google Scholar
- [BHK08]Briest, P., Hoefer, M., Krysta, P.: Stackelberg network pricing games. In: Proc. 25th International Symposium on Theoretical Aspects of Computer Science (STACS), pp. 133–142 (2008)Google Scholar
- [DHK09]Demaine, E.D., Hajiaghayi, M., Kawarabayashi, K.: Approximation algorithms via structural results for apex-minor-free graphs. In: Proc. 36th International Colloquium on Automata, Languages and Programming, ICALP (2009)Google Scholar
- [DHM07]Demaine, E.D., Hajiaghayi, M., Mohar, B.: Approximation algorithms via contraction decomposition. In: Proc. 18th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 278–287 (2007)Google Scholar
- [Kle06]Klein, P.N.: A subset spanner for planar graphs, with application to subset TSP. In: Proc. 38th ACM Symposium on Theory of Computing (STOC), pp. 749–756 (2006)Google Scholar