2,210 research outputs found
Optimal Networks from Error Correcting Codes
To address growth challenges facing large Data Centers and supercomputing
clusters a new construction is presented for scalable, high throughput, low
latency networks. The resulting networks require 1.5-5 times fewer switches,
2-6 times fewer cables, have 1.2-2 times lower latency and correspondingly
lower congestion and packet losses than the best present or proposed networks
providing the same number of ports at the same total bisection. These advantage
ratios increase with network size. The key new ingredient is the exact
equivalence discovered between the problem of maximizing network bisection for
large classes of practically interesting Cayley graphs and the problem of
maximizing codeword distance for linear error correcting codes. Resulting
translation recipe converts existent optimal error correcting codes into
optimal throughput networks.Comment: 14 pages, accepted at ANCS 2013 conferenc
A Graph Theoretical Approach to Network Encoding Complexity
Consider an acyclic directed network with sources and
distinct sinks . For , let denote the
min-cut between and . Then, by Menger's theorem, there exists a
group of edge-disjoint paths from to , which will be referred
to as a group of Menger's paths from to in this paper. Although
within the same group they are edge-disjoint, the Menger's paths from different
groups may have to merge with each other. It is known that by choosing Menger's
paths appropriately, the number of mergings among different groups of Menger's
paths is always bounded by a constant, which is independent of the size and the
topology of . The tightest such constant for the all the above-mentioned
networks is denoted by when all 's are
distinct, and by when all 's are in
fact identical. It turns out that and are closely
related to the network encoding complexity for a variety of networks, such as
multicast networks, two-way networks and networks with multiple sessions of
unicast. Using this connection, we compute in this paper some exact values and
bounds in network encoding complexity using a graph theoretical approach.Comment: 44 pages, 22 figure
Measuring and Understanding Throughput of Network Topologies
High throughput is of particular interest in data center and HPC networks.
Although myriad network topologies have been proposed, a broad head-to-head
comparison across topologies and across traffic patterns is absent, and the
right way to compare worst-case throughput performance is a subtle problem.
In this paper, we develop a framework to benchmark the throughput of network
topologies, using a two-pronged approach. First, we study performance on a
variety of synthetic and experimentally-measured traffic matrices (TMs).
Second, we show how to measure worst-case throughput by generating a
near-worst-case TM for any given topology. We apply the framework to study the
performance of these TMs in a wide range of network topologies, revealing
insights into the performance of topologies with scaling, robustness of
performance across TMs, and the effect of scattered workload placement. Our
evaluation code is freely available
Forbidden induced subgraphs and the price of connectivity for feedback vertex set.
Let fvs(G) and cfvs(G) denote the cardinalities of a minimum feedback vertex set and a minimum connected feedback vertex set of a graph G, respectively. For a graph class G, the price of connectivity for feedback vertex set (poc-fvs) for G is defined as the maximum ratio cfvs(G)/fvs(G) over all connected graphs G in G. It is known that the poc-fvs for general graphs is unbounded. We study the poc-fvs for graph classes defined by a finite family H of forbidden induced subgraphs. We characterize exactly those finite families H for which the poc-fvs for H-free graphs is bounded by a constant. Prior to our work, such a result was only known for the case where |H|=1
On the Cost of Participating in a Peer-to-Peer Network
In this paper, we model the cost incurred by each peer participating in a
peer-to-peer network. Such a cost model allows to gauge potential disincentives
for peers to collaborate, and provides a measure of the ``total cost'' of a
network, which is a possible benchmark to distinguish between proposals. We
characterize the cost imposed on a node as a function of the experienced load
and the node connectivity, and show how our model applies to a few proposed
routing geometries for distributed hash tables (DHTs). We further outline a
number of open questions this research has raised.Comment: 17 pages, 4 figures. Short version to be published in the Proceedings
of the Third International Workshop on Peer-to-Peer Systems (IPTPS'04). San
Diego, CA. February 200
Entanglement Routing and Bottlenecks in Grid Networks
In a recent article, Hahn et al. (npj Quantum Inf. 5, 76 (2019)) proposed a
protocol for establishing EPR pairs in quantum networks. They used graph
theoretic tools like local complementation and showed that their protocol can
reduce the number of measurements required compared to standard repeater-based
schemes for the same task. They also showed how local complementation can solve
bottleneck issues in network architectures like the butterfly network. Here we
extend their work, increasing its efficiency and the domain of applicability.
Specifically, we show how the original proof can be modified to incorporate a
wider variety of scenarios and provide examples demonstrating the modified
protocol's advantage. Furthermore, we provide a method to apply recent results
on bottlenecks in ring graphs to illustrate how grid graphs are affected. Using
this, we demonstrate how the butterfly and similar networks suffer from the
same bottleneck issues as ring and line graphs.Comment: An efficient protocol for establishing EPR pairs in quantum networks
is proposed by generalizing the work of Hahn et al. (npj Quantum Inf. 5, 76
(2019)
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