Accelerating Simulated Annealing for the Permanent and Combinatorial Counting Problems

Bezáková, Ivona; Štefankovič, Daniel; Vazirani, Vijay V.; Vigoda, Eric

doi:10.1137/050644033

Cited by 77 publications

(123 citation statements)

References 13 publications

Supporting

Mentioning

118

Contrasting

Order By: Relevance

“…Monte Carlo method. Bezakova et al [19] improve this run-Indeed, when we apply our system-wide metric, we see that ning time to 0(nr7 log4 n) by using a new "cooling schedule" the bipartite graph has only a single perfect matching, thus for the simulated annealing algorithm running on top of the identifying the true communication pattern of the system. Markov chain.…”

Section: The Anonymity System Inmentioning

confidence: 84%

A Combinatorial Approach to Measuring Anonymity

Edman

Sivrikaya

Yener

2007

2007 IEEE Intelligence and Security Informatics

View full text Add to dashboard Cite

In this paper we define a new metric for quantifying formally define our proposed anonymity metric. We then show the degree of anonymity collectively afforded to users of an how our model can be generalized to include probabilistic anonymous communication system. We show how our metric, information in Section III. We demonstrate how to apply our based on the permanent of a matrix, can be useful in evaluating the amount of information needed by an observer to reveal the metio some common type o me istin iV. In communication pattern as a whole. We also show how our model Section V, we compare our metric to some existing metrics to can be extended to include probabilistic information learned illustrate the more important differences. Section VI describes by an attacker about possible sender-recipient relationships. how we can obtain a lower-bound on the anonymity level Our work is intended to serve as a complementary tool to of a system while avoiding some computational complexity existing information-theoretic metrics, which typically consider the anonymity of the system from the perspective of a single user inheren in ctin tnr a or message.conclude in Section VII.A. Related Work Diaz et al. [7] independently proposed a similar entropy-The rest of this paper is structured as follows. First, we will based metric they refer to as the degree of anonymity, a term review some of the previous work done to establish measures first introduced by Reiter and Rubin in the Crowds design [8].Of anonymity. In Section II, we introduce our model and They define the degree of anonymity d as

show abstract

Section: The Anonymity System Inmentioning

confidence: 84%

A Combinatorial Approach to Measuring Anonymity

Edman

Sivrikaya

Yener

2007

2007 IEEE Intelligence and Security Informatics

View full text Add to dashboard Cite

show abstract

“…On the first point, approximation algorithms for the permanent of a matrix are a vigorously studied field of mathematics. Recent improvements include those of Jerrum et al (2004) [7], Bezáková et al (2006) [4], and Huber and Law (2008) [6]; the computational complexities of these methods are O ( n 10 (log n ) 3 ), O ( n 7 (log n ) 4 ), and O ( n 4 log n ), respectively. These dramatic decreases in complexity have been experienced only in the last ten years, and further developments can therefore be expected.…”

Section: Discussionmentioning

confidence: 99%

“…Exact computation of a permanent is #P-complete [3]. A #P class is a set of counting problems that belongs to nondeterministic polynomial time, and a problem is #P-complete if and only if it is in #P. Because it has been proved that the permanent is #P-complete, exact computation of the permanent is not possible in polynomial time, and algorithms for polynomial time approximation have therefore been proposed [4-7]. We employed the Huber–Law algorithm [6], which is, to the best of our knowledge, currently the fastest algorithm when the matrix is dense.…”

Section: Introductionmentioning

confidence: 99%

Application of permanents of square matrices for DNA identification in multiple-fatality cases

2013

View full text Add to dashboard Cite

BackgroundDNA profiling is essential for individual identification. In forensic medicine, the likelihood ratio (LR) is commonly used to identify individuals. The LR is calculated by comparing two hypotheses for the sample DNA: that the sample DNA is identical or related to a reference DNA, and that it is randomly sampled from a population. For multiple-fatality cases, however, identification should be considered as an assignment problem, and a particular sample and reference pair should therefore be compared with other possibilities conditional on the entire dataset.ResultsWe developed a new method to compute the probability via permanents of square matrices of nonnegative entries. As the exact permanent is known as a #P-complete problem, we applied the Huber–Law algorithm to approximate the permanents. We performed a computer simulation to evaluate the performance of our method via receiver operating characteristic curve analysis compared with LR under the assumption of a closed incident. Differences between the two methods were well demonstrated when references provided neither obligate alleles nor impossible alleles. The new method exhibited higher sensitivity (0.188 vs. 0.055) at a threshold value of 0.999, at which specificity was 1, and it exhibited higher area under a receiver operating characteristic curve (0.990 vs. 0.959, P = 9.6E-15).ConclusionsOur method therefore offers a solution for a computationally intensive assignment problem and may be a viable alternative to LR-based identification for closed-incident multiple-fatality cases.

show abstract

“…The normalisation is convenient if one wishes to compare the number of q-colourings in graphs on different numbers of vertices. Inequality (1) is the zero-temperature version of (2) F q G (β) ≤ F q K d,d (β) , since in the limit β → +∞, inequality (2) becomes exactly (1). For general d, Galvin [9,11] showed that (2) holds for all β when G is bipartite, and (1) holds for all d when q ≥ 2 d|V (G)|/2 4 .…”

Section: Introductionmentioning

confidence: 99%

Counting Proper Colourings in 4-Regular Graphs via the Potts Model

Davies

2018

Electron. J. Combin.

View full text Add to dashboard Cite

We give tight upper and lower bounds on the internal energy per particle in the antiferromagnetic q-state Potts model on 4-regular graphs, for q ≥ 5. This proves the first case of a conjecture of the author, Perkins, Jenssen, and Roberts, and implies tight bounds on the antiferromagnetic Potts partition function.The zero-temperature limit gives upper and lower bounds on the number of proper q-colourings of 4-regular graphs, which almost proves the case d = 4 of a conjecture of Galvin and Tetali. For any q ≥ 5 we prove that the number of proper q-colourings of a 4-regular graph is maximised by a union of K4,4's.

show abstract

Accelerating Simulated Annealing for the Permanent and Combinatorial Counting Problems

Cited by 77 publications

References 13 publications

A Combinatorial Approach to Measuring Anonymity

A Combinatorial Approach to Measuring Anonymity

Application of permanents of square matrices for DNA identification in multiple-fatality cases

Counting Proper Colourings in 4-Regular Graphs via the Potts Model

Contact Info

Product

Resources

About