The chairman assignment problem

Tijdeman, R.

doi:10.1016/0012-365x(80)90269-1

Cited by 80 publications

(68 citation statements)

References 2 publications

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“…One of the key non-economic abstractions for resource allocation is a computer science context is Proportional Share (PS), originally documented by Tijdeman [28]. Each PS process i has a weight w i .…”

Section: Related Workmentioning

confidence: 99%

Tycoon: An implementation of a distributed, market-based resource allocation system

Lai

Rasmusson

Adar

et al. 2005

MGS

250

205

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Distributed clusters like the Grid and PlanetLab enable the same statistical multiplexing efficiency gains for computing as the Internet provides for networking. One major challenge is allocating resources in an economically efficient and low-latency way. A common solution is proportional share, where users each get resources in proportion to their pre-defined weight. However, this does not allow users to differentiate the value of their jobs. This leads to economic inefficiency. In contrast, systems that require reservations impose a high latency (typically minutes to hours) to acquire resources.We present Tycoon, a market based distributed resource allocation system based on proportional share. The key advantages of Tycoon are that it allows users to differentiate the value of their jobs, its resource acquisition latency is limited only by communication delays, and it imposes no manual bidding overhead on users. We present experimental results using a prototype implementation of our design.

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Section: Related Workmentioning

confidence: 99%

Tycoon: An implementation of a distributed, market-based resource allocation system

Lai

Rasmusson

Adar

et al. 2005

MGS

250

205

View full text Add to dashboard Cite

show abstract

“…(The allocation stage is also efficient and takes polynomial time.) This contrast most other algorithms that produce smooth schedules (e.g., [12,13,30]) as they are based on priority queues and their time per slot is at least logarithmic in the size of the queues.…”

Section: Smooth and Distributed Schedulingmentioning

confidence: 87%

“…The Chairman Assignment Problem. An early scheduling problem, due to Tijdeman [30], is the following Chairman Assignment Problem. There is a union of several states, each having a positive weight.…”

Section: Related Workmentioning

confidence: 99%

“…This problem is a special case of our flat allocation problem in which the sum of the rates is one and all the slots are required to be allocated. Tijdeman [30] proved that any such problem has a solution with a 2-smooth 5 allocation. Moreover, an algorithm of O(log n) time per slot, where n is the number of states, is implicit in his solution.…”

Section: Related Workmentioning

confidence: 99%

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On Centralized Smooth Scheduling

Litman

Moran-Schein

2009

Algorithmica

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This paper studies evenly distributed sets of natural numbers and their applications to scheduling in a distributed environment. Such sets, called smooth sets, have the property that their quantity within each interval is proportional to the size of the interval, up to a bounded additive deviation; namely, for ρ, ∆ ∈ R a set A of natural numbers is (ρ, ∆)-smooth if abs(|I| · ρ − |I ∩ A|) < ∆ for any interval I ⊂ N.The current paper studies scheduling persistent clients on a single slot-oriented resource in a flexible, predictable and distributed manner. Each client γ has a given rate ρ γ that defines the share of the resource he is entitled to receive and the goal is a smooth schedule in which, for some predefined ∆, each client γ is served in a (ρ γ , ∆)-smooth set of slots (natural numbers). The paper focuses on a distributed environment where each client by itself (without any inter-client communication) resolves (computes), slot after slot, whether or not it owns this slot. The paper presents extremely efficient schedules under which a client resolves each slot in a constant time.The paper considers two scheduling frameworks. The first one, the Flat Scheduling Framework, is the common problem where the rates of the clients are given a priori. In the second and novel framework, the Open-Market Scheduling Framework, fractions of the resource are bought and sold by dealers. Each dealer, upon receiving his fraction, may choose either to become a client and use his share, or to remain a dealer and sell fractions of his share to other dealers. In this framework, the allocation process is highly distributed; moreover, fractions of several resources can be combined into a single virtual resource of new capabilities.The paper presents two scheduling techniques. Both techniques, in both frameworks, produce smooth schedules with highly efficient distributed resolutions -a client resolves each slot in O(1) time on a RAM with a moderate number of memory words, all of a small size. Each technique has its pros and cons. For example, one technique utilizes 100% of the resource but its resolution algorithm requires a number of words which is linear in the number of clients; the other technique utilizes only 99% of the resource but its resolution algorithm requires just O(1) words.One of these techniques yields a solution to Tijdeman's Hierarchial Chairman Assignment Problem which outperforms prior solutions. The other technique naturally extends to the problem of scheduling multiple resources, under the restriction that a client may be served concurrently by at most one resource. The extension yields the first solution to this problem having efficient distributed resolution. Prior solutions produce a special type of smooth scheduling called P-fair scheduling, are centralized, and are less efficient than ours.

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“…In Tijdeman (1980) an optimal solution for the chairman assignment problem was presented for a stronger fairness condition that depends on the prefixes of the schedule. These papers considered unit-length jobs on a single machine.…”

Section: Related Workmentioning

confidence: 99%