Self-organizing sequential search and Hilbert's inequalities
Journal of Computer and System Sciences - 17th Annual ACM Symposium in the Theory of Computing, May 6-8, 1985
The competitiveness of on-line assignments
Journal of Algorithms
Achieving network optima using Stackelberg routing strategies
IEEE/ACM Transactions on Networking (TON)
On-line routing of virtual circuits with applications to load balancing and machine scheduling
Journal of the ACM (JACM)
Scheduling to minimize average completion time: off-line and on-line approximation algorithms
Mathematics of Operations Research
Optimal scheduling of multiclass parallel machines
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Heuristic Algorithms for Scheduling Independent Tasks on Nonidentical Processors
Journal of the ACM (JACM)
Algorithms for Scheduling Tasks on Unrelated Processors
Journal of the ACM (JACM)
A PTAS for Minimizing the Total Weighted Completion Time on Identical Parallel Machines
Mathematics of Operations Research
Scheduling independent tasks to reduce mean finishing time
Communications of the ACM
Convex quadratic and semidefinite programming relaxations in scheduling
Journal of the ACM (JACM)
Stackelberg scheduling strategies
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Tight bounds for worst-case equilibria
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
(Incremental) priority algorithms
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Scheduling Unrelated Machines by Randomized Rounding
SIAM Journal on Discrete Mathematics
Non-approximability Results for Scheduling Problems with Minsum Criteria
Proceedings of the 6th International IPCO Conference on Integer Programming and Combinatorial Optimization
Performance Guarantees of Local Search for Multiprocessor Scheduling
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
Tolls for Heterogeneous Selfish Users in Multicommodity Networks and Generalized Congestion Games
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
The Price of Routing Unsplittable Flow
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
The price of anarchy of finite congestion games
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
How much can taxes help selfish routing?
Journal of Computer and System Sciences - Special issue on network algorithms 2005
(Almost) optimal coordination mechanisms for unrelated machine scheduling
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Fast convergence to nearly optimal solutions in potential games
Proceedings of the 9th ACM conference on Electronic commerce
Efficient coordination mechanisms for unrelated machine scheduling
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Coordination mechanisms for selfish scheduling
Theoretical Computer Science
Intrinsic robustness of the price of anarchy
Proceedings of the forty-first annual ACM symposium on Theory of computing
Theoretical Computer Science
Non-clairvoyant Scheduling Games
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Convergence time to Nash equilibria
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Taxes for linear atomic congestion games
ACM Transactions on Algorithms (TALG)
Nash Equilibria and the Price of Anarchy for Flows over Time
Theory of Computing Systems - Special Issue: Algorithmic Game Theory
Tight bounds for selfish and greedy load balancing
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Improving the price of anarchy for selfish routing via coordination mechanisms
ESA'11 Proceedings of the 19th European conference on Algorithms
The price of anarchy for minsum related machine scheduling
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
Preemptive coordination mechanisms for unrelated machines
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Smooth inequalities and equilibrium inefficiency in scheduling games
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
Optimal Cost Sharing for Resource Selection Games
Mathematics of Operations Research
NP-hardness of pure Nash equilibrium in Scheduling and Network Design Games
Theoretical Computer Science
Coordination mechanisms from (almost) all scheduling policies
Proceedings of the 5th conference on Innovations in theoretical computer science
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We study coordination mechanisms aiming to minimize the weighted sum of completion times of jobs in the context of selfish scheduling problems. Our goal is to design local policies that achieve a good price of anarchy in the resulting equilibria for unrelated machine scheduling. To obtain these approximation bounds, we introduce a new technique that while conceptually simple, seems to be quite powerful. The method entails mapping strategy vectors into a carefully chosen inner product space; costs are shown to correspond to the norm in this space, and the Nash condition also has a simple description. With this structure in place, we are able to prove a number of results, as follows. First, we consider Smith's Rule, which orders the jobs on a machine in ascending processing time to weight ratio, and show that it achieves an approximation ratio of 4. We also demonstrate that this is the best possible for deterministic non-preemptive strongly local policies. Since Smith's Rule is always optimal for a given fixed assignment, this may seem unsurprising, but we then show that better approximation ratios can be obtained if either preemption or randomization is allowed. We prove that ProportionalSharing, a preemptive strongly local policy, achieves an approximation ratio of 2.618 for the weighted sum of completion times, and an approximation ratio of 2.5 in the unweighted case. We also observe that these bounds are tight. Next, we consider Rand, a natural non-preemptive but randomized policy. We show that it achieves an approximation ratio of at most 2.13; moreover, if the sum of the weighted completion times is negligible compared to the cost of the optimal solution, this improves to π/2. Finally, we show that both ProportionalSharing and Rand induce potential games, and thus always have a pure Nash equilibrium (unlike Smith's Rule). This allows us to design the first combinatorial constant-factor approximation algorithm minimizing weighted completion time for unrelated machine scheduling. It achieves a factor of 2+ε for any ε 0, and involves imitating best response dynamics using a variant of ProportionalSharing as the policy.