5,950 research outputs found
Space-Efficient Routing Tables for Almost All Networks and the Incompressibility Method
We use the incompressibility method based on Kolmogorov complexity to
determine the total number of bits of routing information for almost all
network topologies. In most models for routing, for almost all labeled graphs
bits are necessary and sufficient for shortest path routing. By
`almost all graphs' we mean the Kolmogorov random graphs which constitute a
fraction of of all graphs on nodes, where is an arbitrary
fixed constant. There is a model for which the average case lower bound rises
to and another model where the average case upper bound
drops to . This clearly exposes the sensitivity of such bounds
to the model under consideration. If paths have to be short, but need not be
shortest (if the stretch factor may be larger than 1), then much less space is
needed on average, even in the more demanding models. Full-information routing
requires bits on average. For worst-case static networks we
prove a lower bound for shortest path routing and all
stretch factors in some networks where free relabeling is not allowed.Comment: 19 pages, Latex, 1 table, 1 figure; SIAM J. Comput., To appea
Reversibility in Queueing Models
In stochastic models for queues and their networks, random events evolve in
time. A process for their backward evolution is referred to as a time reversed
process. It is often greatly helpful to view a stochastic model from two
different time directions. In particular, if some property is unchanged under
time reversal, we may better understand that property. A concept of
reversibility is invented for this invariance. Local balance for a stationary
Markov chain has been used for a weaker version of the reversibility. However,
it is still too strong for queueing applications.
We are concerned with a continuous time Markov chain, but dose not assume it
has the stationary distribution. We define reversibility in structure as an
invariant property of a family of the set of models under certain operation.
The member of this set is a pair of transition rate function and its supporting
measure, and each set represents dynamics of queueing systems such as arrivals
and departures. We use a permutation {\Gamma} of the family menmbers, that is,
the sets themselves, to describe the change of the dynamics under time
reversal. This reversibility is is called {\Gamma}-reversibility in structure.
To apply these definitions, we introduce new classes of models, called
reacting systems and self-reacting systems. Using those definitions and models,
we give a unified view for queues and their networks which have reversibility
in structure, and show how their stationary distributions can be obtained. They
include symmetric service, batch movements and state dependent routing.Comment: Submitted for publicatio
A new scheme to realize crosstalk-free permutations in optical MINs with vertical stacking
©2002 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.Vertical stacking is an alternative for constructing nonblocking multistage interconnection networks (MINs). In this paper, we study the crosstalk-free permutation in rearrangeable, self-routing Banyan-type optical MINs built on vertical stacking and propose a new scheme for realizing permutations in this class of optical MINs crosstalk-free. The basic idea of the new scheme is to classify permutations into permutation classes such that all permutations in one class share the same crosstalk-free decomposition pattern. By running the Euler-Split based crosstalk-free decomposition only once for a permutation class and applying the obtained crosstalk-free decomposition pattern to all permutations in the class, crosstalk-free decomposition of permutations can be realized in a more efficient way. We show that the number of permutations in a permutation class is huge, enabling the average time complexity of the new scheme to realize a crosstalk-free permutation in an N by N network to be reduced to O(N) from previously O(NlogN).Xiaohong Jiang, Hong Shen, Md. Mamun-ur-Rashid Khandker, Susumu Horiguch
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