Nguyen Kim Thang

Smooth inequalities and equilibrium inefficiency in scheduling games

We study coordination mechanisms for Scheduling Games (with unrelated machines). In these games, each job represents a player, who needs to choose a machine for its execution, and intends to complete earliest possible. In the paper, we focus on a general class of lk-norm (for parameter k) on job completion times as social cost, that permits to balance overall quality of service and fairness. Our goal is to design scheduling policies that always admit a pure Nash equilibrium and guarantee a small price of anarchy for the lk-norm social cost. We consider strongly-local and local policies (the policies with different amount of knowledge about jobs). First, we study the inefficiency in lk-norm social costs of a strongly-local policy SPT that schedules the jobs non-preemptively in order of increasing processing times. We show that the price of anarchy of policy SPT is

Improved local search for universal facility location

O(k^{\frac{k+1}{k}})

Throughput maximization in multiprocessor speed-scaling

and this bound is optimal (up to a constant) for all deterministic, non-preemptive, strongly-local and non-waiting policies (non-waiting policies produce schedules without idle times). Second, we consider the makespan (l∞-norm) social cost by making connection within the lk-norm functions. We present a local policy Balance. This policy guarantees a price of anarchy of O(logm), which makes it the currently best known policy among the anonymous local policies that always admit a pure Nash equilibrium.

NP-hardness of pure Nash equilibrium in Scheduling and Network Design Games

We consider the universal facility location problem in which the goal is to assign clients to facilities in order to minimize the sum of connection and facility costs. The connection cost is proportional to the distance each client has to travel to its assigned facility, whereas the cost of a facility is a non-decreasing function depending on the number of clients assigned to the facility. This model generalizes several variants of facility location problems. We present a

Approximating k -Forest with Resource Augmentation: A Primal-Dual Approach

(5.83 + \epsilon )

Online Primal-Dual Algorithms with Configuration Linear Programs.

(5.83+ϵ) approximation algorithm for this problem based on local search technique.

Improved Local Search for Universal Facility Location

In the classical energy minimization problem, introduced in 24, we are given a set of n jobs each one characterized by its release date, its deadline, its processing volume and we aim to find a feasible schedule of the jobs on a single speed-scalable machine so that the total energy consumption is minimized. Here, we study the throughput maximization version of the problem where we are given a budget of energy E and where every job has also a value. Our goal is to determine a feasible schedule maximizing the (weighted) throughput of the jobs that are executed between their respective release dates and deadlines. We first consider the preemptive non-migratory multiprocessor case in a fully heterogeneous environment in which every job has a machine-dependent release date, deadline and processing volume and every machine obeys to a different speed-to-power function. We present a polynomial time greedy algorithm based on the primal-dual scheme that approximates the optimum solution within a factor depending on the energy functions (the factor is constant for typical energy functions of form P ( z ) = z α ). Then, we focus on the non-preemptive case for which we consider a fixed number of identical parallel machines and two important families of instances: (1) equal processing volume jobs; and (2) agreeable jobs. For both cases we present optimal pseudo-polynomial-time algorithms.

Online Non-Preemptive Scheduling to Minimize Weighted Flow-time on Unrelated Machines

We apply systematically a framework to settle the NP-hardness of some properties related to pure Nash equilibrium in Scheduling and Network Design Games. The technique is simple: first, we construct a gadget without a desired property and then embed it into a larger game which encodes a NP-hard problem in order to prove the complexity of the desired property in a game. This technique is very efficient in proving NP-hardness of the existence of a Nash equilibrium. In the paper, we illustrate the efficiency of the technique in proving the NP-hardness of the existence of a pure Nash equilibrium in Matrix Scheduling Games and Weighted Network Design Games. Moreover, using the technique, we can settle not only the complexity of the equilibrium existence but also that of the existence of good cost-sharing protocol.