Proceedings ArticleDOI
Polynomial time algorithms for network information flow
Peter Sanders,Sebastian Egner,Ludo Tolhuizen +2 more
- pp 286-294
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TLDR
The main result are polynomial time algorithms for constructing coding schemes for multicasting at the maximal data rate and graphs where without coding the rate must be a factor Ω(log|V|) smaller.Abstract:
The famous max-flow min-cut theorem states that a source node s can send information through a network (V,E) to a sink node t at a data rate determined by the min-cut separating s and t. Recently it has been shown that this rate can also be achieved for multicasting to several sinks provided that the intermediate nodes are allowed to reencode the information they receive. In contrast, we present graphs where without coding the rate must be a factor Ω(log|V|) smaller. However, so far no fast algorithms for constructing appropriate coding schemes were known. Our main result are polynomial time algorithms for constructing coding schemes for multicasting at the maximal data rate.read more
Citations
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Journal ArticleDOI
Linear network coding
TL;DR: This work forms this multicast problem and proves that linear coding suffices to achieve the optimum, which is the max-flow from the source to each receiving node.
Journal ArticleDOI
A Random Linear Network Coding Approach to Multicast
TL;DR: This work presents a distributed random linear network coding approach for transmission and compression of information in general multisource multicast networks, and shows that this approach can take advantage of redundant network capacity for improved success probability and robustness.
Journal ArticleDOI
Network Coding for Distributed Storage Systems
TL;DR: It is shown that there is a fundamental tradeoff between storage and repair bandwidth which is theoretically characterize using flow arguments on an appropriately constructed graph and regenerating codes are introduced that can achieve any point in this optimal tradeoff.
Posted Content
Network Coding for Distributed Storage Systems
TL;DR: In this paper, the authors introduce a general technique to analyze storage architectures that combine any form of coding and replication, as well as presenting two new schemes for maintaining redundancy using erasure codes.
Journal ArticleDOI
Polynomial time algorithms for multicast network code construction
Sidharth Jaggi,Peter Sanders,Philip A. Chou,Michelle Effros,Sebastian Egner,K. Jain,Ludo Tolhuizen +6 more
TL;DR: Deterministic polynomial time algorithms and even faster randomized algorithms for designing linear codes for directed acyclic graphs with edges of unit capacity are given and extended to integer capacities and to codes that are tolerant to edge failures.
References
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Journal ArticleDOI
Network information flow
TL;DR: This work reveals that it is in general not optimal to regard the information to be multicast as a "fluid" which can simply be routed or replicated, and by employing coding at the nodes, which the work refers to as network coding, bandwidth can in general be saved.
Journal ArticleDOI
Linear network coding
TL;DR: This work forms this multicast problem and proves that linear coding suffices to achieve the optimum, which is the max-flow from the source to each receiving node.
Journal ArticleDOI
An algebraic approach to network coding
Ralf Koetter,Muriel Medard +1 more
TL;DR: For the multicast setup it is proved that there exist coding strategies that provide maximally robust networks and that do not require adaptation of the network interior to the failure pattern in question.
Journal ArticleDOI
Matrix multiplication via arithmetic progressions
Don Coppersmith,Shmuel Winograd +1 more
TL;DR: In this article, a new method for accelerating matrix multiplication asymptotically is presented, based on the ideas of Volker Strassen, by using a basic trilinear form which is not a matrix product.