Generating connected acyclic digraphs uniformly at random

Mélançon, Guy; Philippe, Fabrice

doi:10.1016/j.ipl.2003.06.002

Cited by 46 publications

(34 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Analysis of the network topologies in Set I suggests that these networks have too many links; for one network, n l =4n n , and for the other, n l =3n n . In the Graph Drawing Community, graphs (i.e., networks) having n l =4n n links are actually considered to be dense [25]. In such a network with dense links, it is easy to achieve a relatively small target rate without network coding.…”

Section: B the Experimental Results Of Sncpmentioning

confidence: 99%

“…The networks in Set I were actually generated by the algorithm in [25], which constructs connected acyclic directed graphs uniformly at random. Two networks with parameters (20 nodes, 80 links, 12 sinks, rate 4) and (40 nodes, 120 links, 12 sinks, rate 3), denoted as SCase 1 and SCase 2, were used for simulations in Set I.…”

Section: A the Setup Of The Experimentsmentioning

confidence: 99%

See 1 more Smart Citation

An effective genetic algorithm for network coding

Leeson²,

Hines³

2012

Computers & Operations Research

View full text Add to dashboard Cite

Abstract-The network coding problem (NCP), which aims to minimize network coding resources such as nodes and links, is a relatively new application of genetic algorithms (GAs) and hence little work has so far been reported in this area. Most of the existing literature on NCP has concentrated primarily on the static network coding problem (SNCP). There is a common assumption in work to date that a target rate is always achievable at every sink as long as coding is allowed at all nodes. In most real-world networks, such as wireless networks, any link could be disconnected at any time. This implies that every time a change occurs in the network topology, a new target rate must be determined. The SNCP software implementation then has to be re-run to try to optimize the coding based on the new target rate. In contrast, the GA proposed in this paper is designed with the dynamic network coding problem (DNCP) as the major concern. To this end, a more general formulation of the NCP is described. The new NCP model considers not only the minimization of network coding resources but also the maximization of the rate actually achieved at sinks. This is particularly important to the DNCP, where the target rate may become unachievable due to network topology changes. Based on the new NCP model, an effective GA is designed by integrating selected new problem-specific heuristic rules into the evolutionary process in order to better diversify chromosomes. In dynamic environments, the new GA does not need to recalculate target rate and also exhibits some degree of robustness against network topology changes. Comparative experiments on both SNCP and DNCP illustrate the effectiveness of our new model and algorithm.

show abstract

Section: B the Experimental Results Of Sncpmentioning

confidence: 99%

Section: A the Setup Of The Experimentsmentioning

confidence: 99%

An effective genetic algorithm for network coding

Leeson²,

Hines³

2012

Computers & Operations Research

View full text Add to dashboard Cite

show abstract

“…We also evaluate the performance of our algorithm based on the two topologies generated by the algorithm in [11] with the following parameters: (50 nodes, 87 links, 10 sinks, rate 5) and (75 nodes, 156 links, 15 sinks, rate 7), which are also experimented in [2], [8]. For the first network with 50 nodes, the obtained front is shown in Fig.…”

Section: Resultsmentioning

confidence: 99%

On the Coding-Link Cost Tradeoff in Multicast Network Coding

Kim

Médard

Aggarwal

et al. 2007

MILCOM 2007 - IEEE Military Communications Conference

View full text Add to dashboard Cite

Abstract-We investigate the issue of the tradeoff between network coding and link usage in multicast network coding. Network coding makes minimum-cost multicast, an NP-complete problem with traditional routing alone, polynomially solvable, but if we consider the network coding capability as a resource, the link cost is actually minimized at the expense of the coding cost. We show that identifying such a tradeoff is NP-hard. For this problem, we propose an evolutionary approach that generalizes our previously proposed algorithms for coding resource optimization. Based on an existing multi-objective genetic algorithm, we develop a novel selection mechanism that utilizes some specific characteristics of the problem. We then show that the algorithm can be implemented in a distributed manner and evaluate the algorithm's performance by performing experiments on several topologies.

show abstract

“…Moves which would create a cycle are rejected and can be checked in a time between O(n) and O(n 2 ) with a typical O(n log(n)) behaviour (Alon and Rodeh, 1978) which here would depend on the higher scoring DAGs. A reversal move can also be introduced (Melançon and Philippe, 2004). Alternatively, Giudici and Castelo (2003) keep track of the ancestor matrix which allows them to check whether the moves are legal in O(n).…”

Section: Appendix a Comparison Of The Different Mcmc Methodsmentioning

confidence: 99%

Partition MCMC for Inference on Acyclic Digraphs

Kuipers

Moffa

2017

Journal of the American Statistical Association

View full text Add to dashboard Cite

Acyclic digraphs are the underlying representation of Bayesian networks, a widely used class of probabilistic graphical models. Learning the underlying graph from data is a way of gaining insights about the structural properties of a domain. Structure learning forms one of the inference challenges of statistical graphical models.MCMC methods, notably structure MCMC, to sample graphs from the posterior distribution given the data are probably the only viable option for Bayesian model averaging. Score modularity and restrictions on the number of parents of each node allow the graphs to be grouped into larger collections, which can be scored as a whole to improve the chain's convergence. Current examples of algorithms taking advantage of grouping are the biased order MCMC, which acts on the alternative space of permuted triangular matrices, and non ergodic edge reversal moves.Here we propose a novel algorithm, which employs the underlying combinatorial structure of DAGs to define a new grouping. As a result convergence is improved compared to structure MCMC, while still retaining the property of producing an unbiased sample. Finally the method can be combined with edge reversal moves to improve the sampler further.

show abstract

Generating connected acyclic digraphs uniformly at random

Abstract: We describe a simple algorithm based on a Markov chain process to generate simply connected acyclic directed graphs over a fixed set of vertices. This algorithm is an extension of a previous one, designed to generate acyclic digraphs, non-necessarily connected.

Cited by 46 publications

References 7 publications

An effective genetic algorithm for network coding

An effective genetic algorithm for network coding

On the Coding-Link Cost Tradeoff in Multicast Network Coding

Partition MCMC for Inference on Acyclic Digraphs

Contact Info

Product

Resources

About