Packet Forwarding Algorithms in a Line Network

Antoniadis, Antonios; Barcelo, Neal; Cole, Daniel G.; Fox, Kyle; Moseley, Benjamin; Nugent, Michael; Pruhs, Kirk

doi:10.1007/978-3-642-54423-1_53

Cited by 8 publications

(14 citation statements)

References 32 publications

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“…What can be shown for different objectives such as maximum flow time or the k -norms of flow time? As mentioned, the work by Antoniadis et al [5] has addressed this case when the graph is a line network in what corresponds to our identical setting when all jobs have unit size. They also showed that the objective of maximum flow time becomes hard in this setting if the network is a tree.…”

Section: Resultsmentioning

confidence: 96%

“…These works differ from ours because we requires all job (packets) to be completely processed and we consider the flow time objective over all the packets. One recent work [5] has considered minimizing total flow time when routing in a line network. Here for total flow time, no positive results were shown, but it was shown that no algorithm can be O(1)-competitive, giving evidence that the problem is algorithmically challenging.…”

Section: Related Workmentioning

confidence: 99%

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Scheduling in Bandwidth Constrained Tree Networks

Moseley

2015

Proceedings of the 27th ACM Symposium on Parallelism in Algorithms and Architectures

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In this paper we introduce a new network scheduling model. Here jobs need to be sent via routers on a tree to machines to be scheduled, and the communication is constrained by network bandwidth. The scheduler coordinates network communication and job machine scheduling. This type of scheduler is highly desirable in practice; yet few works have considered combing networking with job processing. We consider the popular objective of total flow time in the online setting. We give a (1+ )-speed O( 1 7 )-competitive algorithm when all routers are identical and all machines are identical for any fixed > 0. Then we go on to show a (2 + )-speed O( 1 7 )-competitive algorithm when the routers are identical and the machines are unrelated. To show these results we introduce an interesting combination of potential function and dual fitting techniques as well as a reduction of general tree scheduling to a special case of trees.

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Section: Resultsmentioning

confidence: 96%

Section: Related Workmentioning

confidence: 99%

Scheduling in Bandwidth Constrained Tree Networks

Moseley

2015

Proceedings of the 27th ACM Symposium on Parallelism in Algorithms and Architectures

Self Cite

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“…All these works, however, consider minimizing the makespan and assume that the orientation of the graph is fixed. Antoniadis et al [2] also consider average flow time on a directed line. They give lower bounds for competitive ratios in the online setting and O(1) competitive algorithms with resource augmentation for the maximum flow time.…”

Section: Related Workmentioning

confidence: 99%

“…When applying (multiple) timestretches we use the following observation to assess the additional empty space created between jobs: Lemma 6.3. Consider two distinct times T 1 < T 2 with T 1 ∈ I x(1) and T 2 ∈ I x (2) . Applying time-stretches yields shifted times T 1 < T 2 with…”

Section: B Proofs Of Sectionmentioning

confidence: 99%

“…To analyze the set of jobs released within each interval we partition them as follows. A job j released at R x is called small if p j ≤ ε 2 4 |I x | and large otherwise. With this, we partition for each direction d ∈ {r, l} the jobs J d Table 2: Summary of the increased differences between start and completion times of jobs j, k ∈ J, Sj < S k , when stretching start times (denoted by ) or completion times (denoted by ).…”

Section: B Proofs Of Sectionmentioning

confidence: 99%

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Scheduling Bidirectional Traffic on a Path

Disser

Klimm

Lübbecke

2015

Automata, Languages, and Programming

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We study the fundamental problem of scheduling bidirectional traffic along a path composed of multiple segments. The main feature of the problem is that jobs traveling in the same direction can be scheduled in quick succession on a segment, while jobs in opposing directions cannot cross a segment at the same time. We show that this tradeoff makes the problem significantly harder than the related flow shop problem, by proving that it is NP-hard even for identical jobs. We complement this result with a PTAS for a single segment and non-identical jobs. If we allow some pairs of jobs traveling in different directions to cross a segment concurrently, the problem becomes APX-hard even on a single segment and with identical jobs. We give polynomial algorithms for the setting with restricted compatibilities between jobs on a single and any constant number of segments, respectively. * This research was carried out in the framework of Matheon supported by Einstein Foundation Berlin.

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Coordination Mechanisms for Selfish Routing over Time on a Tree

Bhattacharya

Kulkarni

Mirrokni

2014

Automata, Languages, and Programming

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Abstract. While selfish routing has been studied extensively, the problem of designing better coordination mechanisms for routing over time in general graphs has remained an open problem. In this paper, we focus on tree networks (single source multiple destinations) with the goal of minimizing (weighted) average sojourn time of jobs, and provide the first coordination mechanisms with provable price of anarchy for this problem. Interestingly, we achieve our price of anarchy results using simple and strongly local policies such as Shortest Job First and the Smith's Rule (also called HDF). In particular, for the case of unweighted jobs, we design a coordination mechanism with polylogarithmic price of anarchy. For weighted jobs, on the other hand, we show that price of anarchy is a function of the depth of the tree and accompany this result by a lower bound for the price of anarchy for the Smith Rule policy and other common strongly local scheduling policies. Our price of anarchy results also imply improved approximation algorithms for the underlying optimization problem of routing over a tree. This problem is well motivated from applications of routing in supercomputers and data center networks where average sojourn time is an important metric.

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Packet Forwarding Algorithms in a Line Network

Cited by 8 publications

References 32 publications

Scheduling in Bandwidth Constrained Tree Networks

Scheduling in Bandwidth Constrained Tree Networks

Scheduling Bidirectional Traffic on a Path

Coordination Mechanisms for Selfish Routing over Time on a Tree

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