Constant time per edge is optimal on rooted tree networks

In this paper, we consider arbitrary tree networks where every processor, except one, called the root, executes the same program. We show that, to design a depth-first token circulation protocol in such networks, it is necessary to have at least [Formula: see text] configurations, where n is the number of processors in the network and Δi is the degree of processor pi. We then propose a depth-first token circulation algorithm which matches the above minimal number of configurations. We show that the proposed algorithm is self-stabilizing, i.e., the system eventually recovers itself to a legitimate state after any perturbation modifying the state of the processors. Hence, the proposed algorithm is optimal in terms of the number of configurations and no extra cost is involved in making it stabilizing.

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OPTIMALITY AND SELF-STABILIZATION IN ROOTED TREE NETWORKS

Parallel Processing Letters ◽

10.1142/s0129626400000032 ◽

2000 ◽

Vol 10 (01) ◽

pp. 3-14 ◽

Cited By ~ 4

Author(s):

FRANCK PETIT ◽

VINCENT VILLAIN

Keyword(s):

Rooted Tree ◽

The State ◽

Extra Cost ◽

Tree Networks ◽

Token Circulation ◽

Self Stabilization ◽

Legitimate State ◽

Arbitrary Tree

In this paper, we consider arbitrary tree networks where every processor, except one, called the root, executes the same program. We show that, to design a depth-first token circulation protocol in such networks, it is necessary to have at least [Formula: see text] configurations, where n is the number of processors in the network and Δi is the degree of processor pi. We then propose a depth-first token circulation algorithm which matches the above minimal number of configurations. We show that the proposed algorithm is self-stabilizing, i.e., the system eventually recovers itself to a legitimate state after any perturbation modifying the state of the processors. Hence, the proposed algorithm is optimal in terms of the number of configurations and no extra cost is involved in making it stabilizing.

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Constant-Time Filtering Using Shiftable Kernels

IEEE Signal Processing Letters ◽

10.1109/lsp.2011.2167967 ◽

2011 ◽

Vol 18 (11) ◽

pp. 651-654 ◽

Cited By ~ 20

Author(s):

K. N. Chaudhury

Keyword(s):

Constant Time

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A constant-time parallel sorting algorithm and its optical implementation

IEEE Micro ◽

10.1109/40.387690 ◽

1995 ◽

Vol 15 (3) ◽

pp. 60-71 ◽

Cited By ~ 2

Author(s):

A. Louri ◽

J.A. Hatch ◽

Jongwhoa Na

Keyword(s):

Constant Time ◽

Sorting Algorithm ◽

Parallel Sorting

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HTPC: heterogeneous traffic-aware partition coding for random packet spraying in data center networks

Journal of Cloud Computing Advances Systems and Applications ◽

10.1186/s13677-021-00248-4 ◽

2021 ◽

Vol 10 (1) ◽

Author(s):

Jiawei Huang ◽

Shiqi Wang ◽

Shuping Li ◽

Shaojun Zou ◽

Jinbin Hu ◽

...

Keyword(s):

Data Center ◽

Large Scale ◽

Network Performance ◽

Rooted Tree ◽

Heterogeneous Traffic ◽

Data Center Networks ◽

Packet Reordering ◽

Traffic Characteristics ◽

Network Utilization ◽

The Impact

AbstractModern data center networks typically adopt multi-rooted tree topologies such leaf-spine and fat-tree to provide high bisection bandwidth. Load balancing is critical to achieve low latency and high throughput. Although the per-packet schemes such as Random Packet Spraying (RPS) can achieve high network utilization and near-optimal tail latency in symmetric topologies, they are prone to cause significant packet reordering and degrade the network performance. Moreover, some coding-based schemes are proposed to alleviate the problem of packet reordering and loss. Unfortunately, these schemes ignore the traffic characteristics of data center network and cannot achieve good network performance. In this paper, we propose a Heterogeneous Traffic-aware Partition Coding named HTPC to eliminate the impact of packet reordering and improve the performance of short and long flows. HTPC smoothly adjusts the number of redundant packets based on the multi-path congestion information and the traffic characteristics so that the tailing probability of short flows and the timeout probability of long flows can be reduced. Through a series of large-scale NS2 simulations, we demonstrate that HTPC reduces average flow completion time by up to 60% compared with the state-of-the-art mechanisms.

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