15,238 research outputs found
Forwarding and optical indices of 4-regular circulant networks
An all-to-all routing in a graph is a set of oriented paths of , with
exactly one path for each ordered pair of vertices. The load of an edge under
an all-to-all routing is the number of times it is used (in either
direction) by paths of , and the maximum load of an edge is denoted by
. The edge-forwarding index is the minimum of
over all possible all-to-all routings , and the arc-forwarding index
is defined similarly by taking direction into
consideration, where an arc is an ordered pair of adjacent vertices. Denote by
the minimum number of colours required to colour the paths of such
that any two paths having an edge in common receive distinct colours. The
optical index is defined to be the minimum of over all possible
, and the directed optical index is defined
similarly by requiring that any two paths having an arc in common receive
distinct colours. In this paper we obtain lower and upper bounds on these four
invariants for -regular circulant graphs with connection set , . We give approximation algorithms with performance ratio a
small constant for the corresponding forwarding index and routing and
wavelength assignment problems for some families of -regular circulant
graphs.Comment: 19 pages, no figure in Journal of Discrete Algorithms 201
With Great Speed Come Small Buffers: Space-Bandwidth Tradeoffs for Routing
We consider the Adversarial Queuing Theory (AQT) model, where packet arrivals
are subject to a maximum average rate and burstiness
. In this model, we analyze the size of buffers required to avoid
overflows in the basic case of a path. Our main results characterize the space
required by the average rate and the number of distinct destinations: we show
that space suffice, where is the number of distinct
destinations and ; and we show that space is necessary. For directed trees, we describe an algorithm
whose buffer space requirement is at most where is the
maximum number of destinations on any root-leaf path
Methods and problems of wavelength-routing in all-optical networks
We give a survey of recent theoretical results obtained for wavelength-routing in all-optical networks. The survey is based on the previous survey in [Beauquier, B., Bermond, J-C., Gargano, L., Hell, P., Perennes, S., Vaccaro, U.: Graph problems arising from wavelength-routing in all-optical networks. In: Proc. of the 2nd Workshop on Optics and Computer Science, part of IPPS'97, 1997]. We focus our survey on the current research directions and on the used methods. We also state several open problems connected with this line of research, and give an overview of several related research directions
A Practical Scheme for Wireless Network Operation
In many problems in wireline networks, it is known that achieving capacity on each link or subnetwork is optimal for the entire network operation. In this paper, we present examples of wireless networks in which decoding and achieving capacity on certain links or subnetworks gives us lower rates than other simple schemes, like forwarding. This implies that the separation of channel and network coding that holds for many classes of wireline networks does not, in general, hold for wireless networks. Next, we consider Gaussian and erasure wireless networks where nodes are permitted only two possible operations: nodes can either decode what they receive (and then re-encode and transmit the message) or simply forward it. We present a simple greedy algorithm that returns the optimal scheme from the exponential-sized set of possible schemes. This algorithm will go over each node at most once to determine its operation, and hence, is very efficient. We also present a decentralized algorithm whose performance can approach the optimum arbitrarily closely in an iterative fashion
QuickCast: Fast and Efficient Inter-Datacenter Transfers using Forwarding Tree Cohorts
Large inter-datacenter transfers are crucial for cloud service efficiency and
are increasingly used by organizations that have dedicated wide area networks
between datacenters. A recent work uses multicast forwarding trees to reduce
the bandwidth needs and improve completion times of point-to-multipoint
transfers. Using a single forwarding tree per transfer, however, leads to poor
performance because the slowest receiver dictates the completion time for all
receivers. Using multiple forwarding trees per transfer alleviates this
concern--the average receiver could finish early; however, if done naively,
bandwidth usage would also increase and it is apriori unclear how best to
partition receivers, how to construct the multiple trees and how to determine
the rate and schedule of flows on these trees. This paper presents QuickCast, a
first solution to these problems. Using simulations on real-world network
topologies, we see that QuickCast can speed up the average receiver's
completion time by as much as while only using more
bandwidth; further, the completion time for all receivers also improves by as
much as faster at high loads.Comment: [Extended Version] Accepted for presentation in IEEE INFOCOM 2018,
Honolulu, H
- …