Ahuva Mu'alem

Utilization, predictability, workloads, and user runtime estimates in scheduling the IBM SP2 with backfilling

Scheduling jobs on the IBM SP2 system and many other distributed-memory MPPs is usually done by giving each job a partition of the machine for its exclusive use. Allocating such partitions in the o...Scheduling jobs on the IBM SP2 system and many other distributed-memory MPPs is usually done by giving each job a partition of the machine for its exclusive use. Allocating such partitions in the order in which the jobs arrive (FCFS scheduling) is fair and predictable, but suffers from severe fragmentation, leading to low utilization. This situation led to the development of the EASY scheduler which uses aggressive backfilling: Small jobs are moved ahead to fill in holes in the schedule, provided they do not delay the first job in the queue. We compare this approach with a more conservative approach in which small jobs move ahead only if they do not delay any job in the queue and show that the relative performance of the two schemes depends on the workload. For workloads typical on SP2 systems, the aggressive approach is indeed better, but, for other workloads, both algorithms are similar. In addition, we study the sensitivity of backfilling to the accuracy of the runtime estimates provided by the users and find a very surprising result. Backfilling actually works better when users overestimate the runtime by a substantial factor.

Envy-Free Allocations for Budgeted Bidders

We study the problem of identifying prices to support a given allocation of items to bidders in an envy-free way. A bidder will envy another bidder if she would prefer to obtain the other bidders item at the price paid by that bidder. Envy-free prices for allocations have been studied extensively; here, we focus on the impact of budgets: beyond their willingness to pay for items, bidders are also constrained by their ability to pay, which may be lower than their willingness. In a recent paper, Aggarwal et al. show that a variant of the Ascending Auction finds a feasible and bidder-optimal assignment and supporting envy-free prices in polynomial time so long as the input satisfies certain non-degeneracy conditions. While this settles the problem of finding a feasible allocation, an auctioneer might sometimes also be interested in a specific allocation of items to bidders. We present two polynomial-time algorithms for this problem, one which finds maximal prices supporting the given allocation (if such prices exist), and another which finds minimal prices. We also prove a structural result characterizing when different allocations are supported by the same minimal price vector.

On Multi-dimensional Envy-Free Mechanisms

We study the problem of fairness design . Specifically, we focus on approximation algorithms for indivisible items with supporting envy-free bundle prices. We present the first polynomial-communication envy-free profit-maximizing combinatorial auctions for general bidders. In this context, envy-free prices can be interpreted as anonymous non-discriminatory prices. Additionally, we study the canonical makespan-minimizing scheduling problem of unrelated machines, in an envy-free manner. For the special case of related machines model we show that tight algorithmic bounds can be achieved.

On the definition of "on-line" in job scheduling problems

The conventional model of on-line scheduling postulates that jobs have non-trivial release dates, and are not known in advance. However, it fails to impose any stability constraints, leading to algorithms and analyses that must deal with unrealistic load conditions arising from trivial release dates as a special case. In an effort to make the model more realistic, we show how stability can be expressed as a simple constraint on release times and processing times. We then give empirical and theoretical justifications that such a constraint can close the gap between the theory and practice. As it turns out, this constraint seems to trivialize the scheduling problem.

The Power of Preemption in Economic Online Markets

In distributed computer networks where resources are under decentralized control, selfish users will generally not work towards one common goal, such as maximizing the overall value provided by the system, but will instead try to strategically maximize their individual benefit. This shifts the scheduling policy in such systems --- the decision about which user may access what resource --- from being a purely algorithmic challenge to the domain of mechanism design. In this paper we will showcase the benefit of allowing preemptionin such economic online settings regarding the performance of market mechanisms by extending the Decentralized Local Greedy Mechanism of Heydenreich et al. [11]. This mechanism was shown to be 3.281-competitive with respect to total weighted completion time if the players act rationally. We show that the preemptive versionof this mechanism is 2-competitive. As a by-product, preemption allows to relax the assumptions on jobs upon which this competitiveness relies. In addition to this worst case analysis, we provide an in-depth empirical analysis of the average case performanceof the original mechanism and its preemptive extension based on real workload traces. Our empirical findings indicate that introducing preemption improves both the utility and the slowdown of the jobs. Furthermore, this improvement does not come at the expense of low-priority jobs.

On the importance of migration for fairness in online grid markets

Computational grids oer users a simple access to tremendous computer resources for solving large scale computing problems. Traditional performance analysis of scheduling algorithms considers overall system performance while fairness analysis focuses on the individual performance each user receives. Until recently, only few grids and cluster systems provided preemptive migration (e.g. [2]), which is the ability of dynamically moving computational tasks across machines during runtime. The emergent technology of virtualization (e.g. [4]) provides o-the-shelf support for migration, thus making the use of this feature more accessible (even across dierent OS’s). In this paper, we study the close relation between migration and fairness. We present fairness and quality of service properties for economic online scheduling algorithms. Under mild assumptions we show that it is impossible to achieve these properties without the use of migration. On the other hand, if zero cost migration is used, then these properties can be satised.