TY - GEN

T1 - The Stackelberg minimum spanning tree game

AU - Cardinal, Jean

AU - Demaine, Erik D.

AU - Fiorini, Samuel

AU - Joret, Gwenaël

AU - Langerman, Stefan

AU - Newman, Ilan

AU - Weimann, Oren

PY - 2007

Y1 - 2007

N2 - We consider a one-round two-player network pricing game, the Stackelberg Minimum Spanning Tree game or STACKMST. The game is played on a graph (representing a network), whose edges are colored either red or blue, and where the red edges have a given fixed cost (representing the competitor's prices). The first player chooses an assignment of prices to the blue edges, and the second player then buys the cheapest possible minimum 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. This game is the minimum spanning tree analog of the well-studied Stackelberg shortest-path game. We analyze the complexity and approximability of the first player's best strategy in STACKMST. In particular, we prove that the problem is APX-hard even if there are only two different red costs, and give an approximation algorithm whose approximation ratio is at most min{k, 3 + 2 In 6,1 + In W}, where k is the number of distinct red costs, b is the number of blue edges, and W is the maximum ratio between red costs. We also give a natural integer linear programming formulation of the problem, and show that the integrality gap of the fractional relaxation asymptotically matches the approximation guarantee of our algorithm.

AB - We consider a one-round two-player network pricing game, the Stackelberg Minimum Spanning Tree game or STACKMST. The game is played on a graph (representing a network), whose edges are colored either red or blue, and where the red edges have a given fixed cost (representing the competitor's prices). The first player chooses an assignment of prices to the blue edges, and the second player then buys the cheapest possible minimum 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. This game is the minimum spanning tree analog of the well-studied Stackelberg shortest-path game. We analyze the complexity and approximability of the first player's best strategy in STACKMST. In particular, we prove that the problem is APX-hard even if there are only two different red costs, and give an approximation algorithm whose approximation ratio is at most min{k, 3 + 2 In 6,1 + In W}, where k is the number of distinct red costs, b is the number of blue edges, and W is the maximum ratio between red costs. We also give a natural integer linear programming formulation of the problem, and show that the integrality gap of the fractional relaxation asymptotically matches the approximation guarantee of our algorithm.

UR - http://www.scopus.com/inward/record.url?scp=38149111964&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-73951-7_7

DO - 10.1007/978-3-540-73951-7_7

M3 - Conference contribution

AN - SCOPUS:38149111964

SN - 3540739483

SN - 9783540739487

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 64

EP - 76

BT - Algorithms and Data Structures - 10th International Workshop, WADS 2007, Proceedings

PB - Springer Verlag

T2 - 10th International Workshop on Algorithms and Data Structures, WADS 2007

Y2 - 15 August 2007 through 17 August 2007

ER -