TY - GEN

T1 - Maximizing the minimum load

T2 - 5th International Workshop on Internet and Network Economics, WINE 2009

AU - Epstein, Leah

AU - Kleiman, Elena

AU - Van Stee, Rob

PY - 2009

Y1 - 2009

N2 - We consider a scheduling problem where each job is controlled by a selfish agent, who is only interested in minimizing its own cost, which is defined as the total load on the machine that its job is assigned to. We consider the objective of maximizing the minimum load (cover) over the machines. Unlike the regular makespan minimization problem, which was extensively studied in a game theoretic context, this problem has not been considered in this setting before. We study the price of anarchy (poa) and the price of stability (pos). We show that on related machines, both these values are unbounded. We then focus on identical machines. We show that the is 1, and we derive tight bounds on the for m≤6 and nearly tight bounds for general m. In particular, we show that the is at least 1.691 for larger m and at most 1.7. Hence, surprisingly, the is less than the for the makespan problem, which is 2. To achieve the upper bound of 1.7, we make an unusual use of weighting functions. Finally, in contrast we show that the mixed grows exponentially with m for this problem, although it is only Θ(logm/loglogm) for the makespan.

AB - We consider a scheduling problem where each job is controlled by a selfish agent, who is only interested in minimizing its own cost, which is defined as the total load on the machine that its job is assigned to. We consider the objective of maximizing the minimum load (cover) over the machines. Unlike the regular makespan minimization problem, which was extensively studied in a game theoretic context, this problem has not been considered in this setting before. We study the price of anarchy (poa) and the price of stability (pos). We show that on related machines, both these values are unbounded. We then focus on identical machines. We show that the is 1, and we derive tight bounds on the for m≤6 and nearly tight bounds for general m. In particular, we show that the is at least 1.691 for larger m and at most 1.7. Hence, surprisingly, the is less than the for the makespan problem, which is 2. To achieve the upper bound of 1.7, we make an unusual use of weighting functions. Finally, in contrast we show that the mixed grows exponentially with m for this problem, although it is only Θ(logm/loglogm) for the makespan.

UR - http://www.scopus.com/inward/record.url?scp=76649137675&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-10841-9_22

DO - 10.1007/978-3-642-10841-9_22

M3 - Conference contribution

AN - SCOPUS:76649137675

SN - 3642108407

SN - 9783642108402

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

SP - 232

EP - 243

BT - Internet and Network Economics - 5th International Workshop, WINE 2009, Proceedings

Y2 - 14 December 2009 through 18 December 2009

ER -