Network Coding Gaps for Completion Times of Multiple Unicasts

@article{Haeupler2020NetworkCG,
  title={Network Coding Gaps for Completion Times of Multiple Unicasts},
  author={Bernhard Haeupler and David Wajc and Goran Zuzic},
  journal={2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)},
  year={2020},
  pages={494-505}
}
We study network coding gaps for the problem of makespan minimization of multiple unicasts. In this problem distinct packets at different nodes in a network need to be delivered to a destination specific to each packet, as fast as possible. The network coding gap specifies how much coding packets together in a network can help compared to the more natural approach of routing. While makespan minimization using routing has been intensely studied for the multiple unicasts problem, no bounds on… Expand
Edge removal in undirected networks
  • M. Langberg, M. Effros
  • Computer Science, Mathematics
  • 2021 IEEE International Symposium on Information Theory (ISIT)
  • 2021
TLDR
This short manuscript proves that for undirected networks, removing a λ-capacity edge decreases the rate by O(λ), which implies that the zero-error capacity region of an Undirected network equals its vanishing- error capacity region. Expand
Universally-optimal distributed algorithms for known topologies
TLDR
This work provides several (equivalent) graph parameters and shows they are tight universal lower bounds for the above problems, fully characterizing their inherent complexity, and implies that algorithms based on the low-congestion shortcut framework match the above lower bound, making them universally optimal if shortcuts are efficiently approximable. Expand

References

SHOWING 1-10 OF 83 REFERENCES
A reduction approach to the multiple-unicast conjecture in network coding
  • Xunrui Yin, Zongpeng Li, Xin Wang
  • Mathematics, Computer Science
  • 2016 IEEE International Symposium on Information Theory (ISIT)
  • 2016
TLDR
A reduction method is proposed to study the multiple-unicast conjecture, and the conjecture for a new class of networks characterized by relations between cut-sets and source-receiver paths is proved, which subsumes the two known types of networks with non-zero max-flow min-cut gaps. Expand
On the advantage of network coding for improving network throughput
TLDR
It is shown that the maximum coding advantage for a given network is equal to the integrality gap of certain linear programming (LP) formulations for a Steiner tree, which holds for both directed as well as undirected networks. Expand
Delay-constrained unicast and the triangle-cast problem
TLDR
The existing upper bound in the literature on the capacity offered by network coding can be a factor of Θ(D) larger than the true capacity where D is the delay bound is tightened significantly to 8 log(D + 1) by proving a new upper bound. Expand
Network Coding in Undirected Networks
TLDR
The theoretical results show that, for a single unicast or broadcast session, there are no improvements with respect to throughput due to network coding, and the benefit of network coding is to significantly facilitate the design of efficient algorithms to compute and achieve such optimal throughput. Expand
Network coding in undirected graphs is either very helpful or not helpful at all
TLDR
It is proved that any undirected network with $k$ source-sink pairs that exhibits a $(1+\varepsilon)$ gap between its MCF rate and its network coding rate can be used to construct a family of graphs whose gap is $\log(|G'|)^c$ for some constant $c < 1$. Expand
A Geometric Perspective to Multiple-Unicast Network Coding
TLDR
A geometric framework is presented for analyzing the multiple-unicast network coding conjecture, which states that for multiple unicast sessions in an undirected network, network coding is equivalent to routing. Expand
A Constant Bound on Throughput Improvement of Multicast Network Coding in Undirected Networks
TLDR
It is proved that in undirected networks, the ratio of achievable multicast throughput with network coding to that without network coding is bounded by a constant ratio of 2, i.e., network coding can at most double the throughput. Expand
Universal Packet Routing with Arbitrary Bandwidths and Transit Times
TLDR
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. Expand
A simpler proof for O(congestion + dilation) packet routing
TLDR
This work provides a more accessible analysis which is based on conditional expectations and guarantees that constant size edge buffers suffice and answers the question whether there is any instance where all schedules need at least (1 + epsilon)*(congestion + dilation) steps, by making use of a probabilistic construction. Expand
Comparing Network Coding with Multicommodity Flow for the k-pairs Communication Problem
Given a graph G = (V, E) and k source-sink pairs of vertices, this papers investigates the maximum rate r at which all pairs can simultaneously communicate. We view this problem from two perspectivesExpand
...
1
2
3
4
5
...