Online Scheduling with Partial Job Values: Does Timesharing or Randomization Help?

Chin, F.; Fung, Stanley P. Y.

doi:10.1007/s00453-003-1025-6

Cited by 83 publications

(84 citation statements)

References 13 publications

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“…The equality in (9) follows trivially from (7). To see that the inequality in (9) holds as well, observe that, by (7), for all j < m,…”

Section: Factmentioning

confidence: 78%

“…The 2-bounded instances give rise to the strongest currently known lower bounds. These are φ ≈ 1.618 for deterministic algorithms [7,12,18], 1.25 for randomized algorithms in the oblivious adversary model [7], and 4/3 in the adaptive adversary model [4]. For 2-bounded instances, algorithms matching these bounds are known [4,6,14].…”

Section: Previous and Related Work Restricted Variantsmentioning

confidence: 99%

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A Universal Randomized Packet Scheduling Algorithm

Jeż

2012

Algorithmica

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We give a memoryless scale-invariant randomized algorithm REMIX for Packet Scheduling that is e/(e − 1)-competitive against an adaptive adversary. REMIX unifies most of previously known randomized algorithms, and its general analysis yields improved performance guarantees for several restricted variants, including the s-bounded instances. In particular, REMIX attains the optimum competitive ratio of 4/3 on 2-bounded instances.Our results are applicable to a more general problem, called Item Collection, in which only the relative order between packets' deadlines is known. REMIX is the optimal memoryless randomized algorithm against adaptive adversary for that problem.

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“…The equality in (9) follows trivially from (7). To see that the inequality in (9) holds as well, observe that, by (7), for all j < m,…”

Section: Factmentioning

confidence: 78%

Section: Previous and Related Work Restricted Variantsmentioning

confidence: 99%

A Universal Randomized Packet Scheduling Algorithm

Jeż

2012

Algorithmica

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show abstract

“…The lower bound φ constructed in [6] for the general model holds as well for agreeable deadline/value instances.…”

Section: The Agreeable Deadline/value Settingmentioning

confidence: 85%

“…The lower bound φ constructed in [6] for the general model holds as well for scheduling packets with agreeable deadlines and MG. We list MG's performance in the agreeable deadline setting here for its optimality and significance. We include this variant for comparison with others.…”

Section: The Agreeable Deadline Settingmentioning

confidence: 99%

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A Comprehensive Study of an Online Packet Scheduling Algorithm

2011

Combinatorial Optimization and Applications

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We study the bounded-delay model for Qualify-of-Service buffer management. Time is discrete. There is a buffer. Unit-length jobs (also called packets) arrive at the buffer over time. Each packet has an integer release time, an integer deadline, and a positive real value. A packet's characteristics are not known to an online algorithm until the packet actually arrives. In each time step, at most one packet can be sent out of the buffer. The objective is to maximize the total value of the packets sent by their respective deadlines in an online manner. An online algorithm's performance is usually measured in terms of competitive ratio, when this online algorithm is compared with a clairvoyant algorithm achieving the best total value. In this paper, we study a simple and intuitive online algorithm. We analyze its performance in terms of competitive ratio for the general model and a few important variants.Keywords: online algorithm, competitive analysis, buffer management, packet scheduling Model DescriptionWe consider the bounded-delay model introduced in [1,2]. Time is discrete. The t-th (time) step presents the time interval (t−1, t]. There is a buffer and unit-length jobs (also called packets) arrive at the buffer over time. Each packet p has an integer release time r p ∈ Z + , an integer deadline d p ∈ Z + , and a positive real value v p ∈ R + . A packet p's characteristics are not known to an online algorithm until p actually arrives at the buffer at time r p . In each step, at most one packet in the buffer can be sent. A packet p is said to be successfully sent at time t if r p ≤ t ≤ d p . The objective is to maximize the total value of the packets that are successfully sent in an online manner.As people have noted, the offline version of this problem can be solved efficiently using the Hungarian algorithm [3] in time O(n 3 ), where n is the number of packets in the input instance.In the framework of competitive analysis which provides worst-case guarantees, an online algorithm's performance is measured in terms of competitive ratio [4]. For a maximization problem, an online algorithm is called c-competitive if for any finite instance, its total value is no less than 1/c times of what an optimal offline algorithm achieves. In competitive analysis, an input instance is allowed to be generated in an adversarial way so as to maximize the competitive ratio. The upper bound of competitive ratio is achieved by some online algorithms. A competitive ratio strictly less than the lower bound cannot be reached by any online algorithm. If an online algorithm has its competitive ratio same as the lower bound, we say that this online algorithm is optimal. For the bounded-delay model, the currently best known result is 2 √ 2 − 1 ≈ 1.828 [5] and the lower bound is (1 + √ 5)/2 ≈ 1.618 [1,6]. If an online algorithm decides which packet to send only based on the contents of its current buffer, and independent of the packets that have already been released and processed, we call it memoryless.In this paper, we study a sim...

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Multiplexing Packets with Arbitrary Deadlines in Bounded Buffers

Azar

Levy

2006

Algorithm Theory – SWAT 2006

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Online Scheduling with Partial Job Values: Does Timesharing or Randomization Help?

Cited by 83 publications

References 13 publications

A Universal Randomized Packet Scheduling Algorithm

A Universal Randomized Packet Scheduling Algorithm

A Comprehensive Study of an Online Packet Scheduling Algorithm

Multiplexing Packets with Arbitrary Deadlines in Bounded Buffers

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