A simpler proof for O(congestion + dilation) packet routing
@article{Rothvoss2012ASP, title={A simpler proof for O(congestion + dilation) packet routing}, author={Thomas Rothvoss}, journal={ArXiv}, year={2012}, volume={abs/1206.3718} }
In the store-and-forward routing problem, packets have to be routed along given paths such that the arrival time of the latest packet is minimized. A groundbreaking result of Leighton, Maggs and Rao says that this can always be done in time O(congestion + dilation), where the congestion is the maximum number of paths using an edge and the dilation is the maximum length of a path. However, the analysis is quite arcane and complicated and works by iteratively improving an infeasible schedule…
15 Citations
Near-Optimal Schedules for Simultaneous Multicasts
- MathematicsICALP
- 2021
A lower bound for multicasts is proved, which shows that there do not always exist schedules of non-trivial length, which means that this length cannot be improved to O(C+D) + o(\log n)$.
Near-Optimal Scheduling of Distributed Algorithms
- Computer SciencePODC
- 2015
This paper presents a distributed algorithm that produces a near-optimal O(congestion + dilation log n) round schedule, after O(dilation log2 n) rounds of pre-computation, and a key challenge in the latter result is to solve the problem with only private randomness, as globally-shared randomness simplifies it significantly.
Coordination Mechanisms for Selfish Routing over Time on a Tree
- Computer ScienceICALP
- 2014
This paper focuses on tree networks, and designs a coordination mechanism with polylogarithmic price of anarchy for weighted jobs and shows that price of Anarchy is a function of the depth of the tree.
Oligopolistic Competitive Packet Routing
- Computer ScienceATMOS
- 2018
This work proves the existence of a pure Nash equilibrium and shows that it can be constructed by sequentially computing an integral earliest arrival flow for each player, and derives several tight bounds on the price of anarchy and theprice of stability in single source games.
Train Scheduling on a Unidirectional Path
- BusinessFSTTCS
- 2017
We formulate what might be the simplest train scheduling problem considered in the literature and show it to be NP-hard. We also give a log-factor randomised algorithm for it. In our problem we have…
Scheduling Trains with Small Stretch on a Unidirectional Line
- Computer ScienceCALDAM
- 2021
It is proved that minimizing max-stretch is NP-hard even on this simple network, and an O(1)-approximation algorithm is given, which can be interpreted as packet scheduling on in-comb, a special case of in-trees.
An efficient load balancing method for ad hoc networks
- Computer ScienceInt. J. Commun. Syst.
- 2018
2 new metrics for ad hoc networks are proposed and defined: bandwidth utilization ratio and load index, which can be used as an indicator to measure and monitor the network usability and to improve its efficiency by efficient load distribution.
Computation-Aware Data Aggregation
- Computer Science, MathematicsITCS
- 2020
A model of distributed computation that considers both computation and communication so as to give a theoretical treatment of data aggregation is introduced and a polynomial-time algorithm is given that computes the optimal schedule when the input network is a complete graph.
The Moser-Tardos Framework with Partial Resampling
- Computer Science2013 IEEE 54th Annual Symposium on Foundations of Computer Science
- 2013
A partial resampling approach that resample an appropriately-random subset of the set of variables that define this event, rather than the entire set as in Moser & Tardos, leads to several improved algorithmic applications in scheduling, graph transversals, packet routing etc.
1 k-uniform Hypergraph Coloring
- Computer Science, Mathematics
- 2019
The probabilistic method is a proof technique for showing the existence of a mathematical object by constructing random objects and then trying to find out if any of the authors' randomly constructed objects do not work.
References
SHOWING 1-10 OF 26 REFERENCES
Fast Algorithms for Finding O(Congestion + Dilation) Packet Routing Schedules
- Computer Science, MathematicsProceedings of the Twenty-Eighth Annual Hawaii International Conference on System Sciences
- 1995
This paper shows how to find a schedule O(c+d) steps using constant-size queues, with probability , for any positive constant β, where is the sum of the lengths of the paths taken by the packets in the network.
Distributed packet switching in arbitrary networks
- Computer ScienceSTOC '96
- 1996
Techniques to guarantee the high probability of dehvering packets without resorting to the Lovi$sz Local Lemma are developed and the distributed algorithm for problems with relatively high dilation is improved.
Universal Packet Routing with Arbitrary Bandwidths and Transit Times
- Computer ScienceIPCO
- 2011
Key to the results is a framework which employs tight bounds for instances where each packet travels along only a small number of edges, which is the first improvement of the bounds for this very fundamental problem in more than 10 years.
Real-Time Message Routing and Scheduling
- Computer ScienceAPPROX-RANDOM
- 2009
This work provides efficient routing strategies yielding origin-destination paths of bounded dilation and congestion and can give good a priori guarantees on the time required to send a given set of messages which implies that all messages can be scheduled to reach their destination on time.
Shortest-Path Routing in Arbitrary Networks
- Computer ScienceJ. Algorithms
- 1999
An on-line protocol which routes any set of packets along shortest paths with congestionCand dilation through an arbitrary network inO(C+D+logN) steps, with high probability, and shows that the preceding bound holds also for random routing problems with the maximum expected congestion over all links.
Packet Routing: Complexity and Algorithms
- Computer ScienceWAOA
- 2009
This paper presents several new ideas and techniques that lead to novel algorithms and hardness results that help to minimize the makespan, i.e., the time at which the last packet arrives at its destination.
A constant-factor approximation algorithm for packet routing, and balancing local vs. global criteria
- Computer ScienceSTOC '97
- 1997
We present the first constant-factor approximation algorithm for a fundamental problem: the store-and-forward packet routing problem on arbitrary networks. Furthermore, the queue sizes required at…
Improved Bounds for Acyclic Job Shop Scheduling
- BusinessComb.
- 2002
The new upper bound is essentially best possible, by proving the existence of instances of acyclic job shop scheduling for which the shortest legal schedule is of length .
Problems and Results on 3-chromatic Hypergraphs and Some Related Questions
- Mathematics
A hypergraphi is a collection of sets. This paper deals with finite hy-pergraphs only. The sets in the hypergraph are called edges, the elements of these edges are points. The degree of a point is…
Universal Routing Strategies for Interconnection Networks
- Computer ScienceLecture Notes in Computer Science
- 1998
This paper presents communication mechanisms used in practice for all-optical networks, including protocol for wormhole routing, and describes the current and future directions for such networks.