92 research outputs found
Speeding up Glauber Dynamics for Random Generation of Independent Sets
The maximum independent set (MIS) problem is a well-studied combinatorial
optimization problem that naturally arises in many applications, such as
wireless communication, information theory and statistical mechanics.
MIS problem is NP-hard, thus many results in the literature focus on fast
generation of maximal independent sets of high cardinality. One possibility is
to combine Gibbs sampling with coupling from the past arguments to detect
convergence to the stationary regime. This results in a sampling procedure with
time complexity that depends on the mixing time of the Glauber dynamics Markov
chain.
We propose an adaptive method for random event generation in the Glauber
dynamics that considers only the events that are effective in the coupling from
the past scheme, accelerating the convergence time of the Gibbs sampling
algorithm
Some examples and counterexamples for (min,+) filtering operations
This paper collects a serie of examples and counterexamples encountered in the study of the algorithmics of Network Calculus operations. Network Calculus is a deterministic queuing theory which aims at providing bounds on the performances of communication networks thanks to a nice formalization in (min,+) algebra. Often presented as a (min,+) filtering theory by analogy with the (+,x) filtering of traditional system theory, it makes use a well-defined set of operations. Their algorithmic aspects have not been much addressed. For this reason, we describe and analyze in a previous report a set of algorithms implementing these Network Calculus operations for a well-chosen class of functions. During this work, we had to construct some examples and counterexamples in order to draw the limits of our results or to illustrate them. Many of them have been omitted in that report and are now presented in this companion-paper
An Algorithmic Toolbox for Network Calculus
Network Calculus offers powerful tools to analyze the performances in communication networks, in particular to obtain deterministic bounds. This theory is based on a strong mathematical ground, notably by the use of (min,+) algebra. However the algorithmic aspects of this theory have not been much addressed yet. This paper is an attempt to provide some efficient algorithms implementing Network Calculus operations for some classical functions. Some functions which are often used are the piecewise affine functions which ultimately have a constant growth. As a first step towards algorithmic design, we present a class containing these functions and closed under the Network Calculus operations: the piecewise affine functions which are ultimately pseudo-periodic. They can be finitely described which enables us to propose some algorithms for each of the Network Calculus operations. We finally analyze their computational complexity
Exact Worst-case Delay in FIFO-multiplexing Feed-forward Networks
In this paper, we compute the actual worst-case end-to-end delay for a flow in a feed-forward network of first-in–first-out (FIFO)-multiplexing service curve nodes, where flows are shaped by piecewise-affine concave arrival curves, and service curves are piecewise affine and convex. We show that the worst-case delay problem can be formulated as a mixed integer linear programming problem, whose size grows exponentially with the number of nodes involved. Furthermore, we present approximate solution schemes to find upper and lower delay bounds on the worst-case delay. Both only require to solve just one linear programming problem and yield bounds that are generally more accurate than those found in the previous work, which are computed under more restrictive assumptions
End-to-end performance guarantees for multipath flows
When routing data across a network from one source to one destination, instead of following a fixed path, one can choose to spread data on several routes in order to use all poten- tial ressources of the network. This issue has been studied for many models of networks with various objectives to opti- mize. In this paper we investigate how to route a flow across a network of servers with end-to-end performance guarantees in the framework of Network Calculus. We discuss stability issues (i.e. whether we can ensure that end-to-end delays are bounded) for arbitrary networks, and how to compute bounds on worst-case end-to-end delays and backlogs. The tightness issues are discussed on a small but challenging toy example
Computation of a (min,+) multi-dimensional convolution for end-to-end performance analyzes
We investigate how to compute a (min,+) multi-dimensional convolution with application to the worst-case performance analyzes in "Pay Multiplexing Only Once" scenarios. In such scenarios, a flow encounters some cross-traffic along its path and each cross-traffic flow interfers over a connected subpath. When there is no cross-traffic, the analyzes boils down to classical (min,+) convolutions. We provide three proofs to a well-known lemma describing how to compute the convolution of piecewise affine convex functions
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