Vorapong Suppakitpaisarn

Parametric Multiroute Flow and Its Application to Robust Network with k Edge Failures

In this work, we investigate properties of the function taking the real value \(h\) to the max \(h\)-route flow value, and apply the result to solve robust network flow problems. We show that the function is piecewise hyperbolic, and modify a parametric optimization technique, the ES algorithm, to find this function. The running time of the algorithm is \(O(\lambda mn)\), when \(\lambda \) is a source-sink edge connectivity of our network, \(m\) is the number of links, and \(n\) is the number of nodes. We can use the result from that algorithm to solve two max-flow problems against \(k\) edge failures, referred to as max-MLA-robust flow and max-MLA-reliable flow. When \(h\) is optimally chosen from the function, we show that the max-\(h\)-route flow is an exact solution of both problems for graphs in a specific class. Our numerical experiments show that \(98\,\%\) of random graphs generated in the experiment are in that specific class. Given a parametric edge \(e\), we also show that the function taking the capacity of \(e\) to the max-\(h\)-route flow value is linear piecewise. Hence we can apply our modified ES algorithm to find that function in \(O(h^2mn)\).

Maximum lifetime coverage problems with battery recovery effects

Scheduling sensors to prolong the lifetime of covering targets in the field is one of the central problems in wireless sensor networks. This problem, called the maximum lifetime coverage problem (MLCP), can be formulated as a linear programming problem with exponential size, and has a constant-factor approximation algorithm. In reality, however, batteries of sensors have recovery effects, which is a phenomenon that the deliverable energy in batteries can be replenished by itself if it is left idling for sufficient duration. Thanks to that effects, we can obtain much longer lifetime of sensors if each sensor is forced to take a sleep at some interval. In this paper, we introduce two models that extend the MLCP, incorporating battery recovery effects. The first model represents battery recovery effects in a deterministic way, while the second one uses a probabilistic model to imitate the effects. We then propose efficient algorithms that work for both models by extending approximation algorithms for the original MLCP. Numerical experiments show that the lifetime of our schedule is 10-40% longer than one without battery recovery effects.

An Approximation Algorithm for Multiroute Flow Decomposition

Abstract In this paper, we give an algorithm to optimize the number of elementary k-flows obtained by decomposing a given k-route flow. It is known that a k-route flow can be decomposed into a linear combination of elementary k-flows, and there are many algorithms proposed for that decomposition. However, the number of elementary k-flows from those algorithms can be as large as O ( | E | ) when | E | is the number of edges in our network. As we have to reroute our flow for each elementary k-flow, it is more desirable to have a smaller number of the elementary flows in the combination. Let v be a maximum k-route flow value of our network, and h be a real number such that 0 h 1 . Denote τ h be the maximum value such that the flow value of the network is h ⋅ v , when edges with flow value less than τ h are removed. We propose an algorithm to decompose a ( v − k ⋅ τ h ⋅ O P T ) / v -fraction of a k-route flow to at most 1 1 − h ⋅ O P T elementary k-flows, when OPT is an optimal number of elementary k-flows required.

Robust network flow against attackers with knowledge of routing method

Recently, many algorithms are proposed to find a communication flow that is robust against k-edges failures. That flow can be weaker, if attackers can obtain forwarding information in each router. In this paper, we propose an algorithm that find a forwarding algorithm maximizing the remaining flow in that situation. We show that Kishimotos multiroute flow is a (k + 1)-approximation algorithm for the problem, when the route number is k + 1. When the route number is optimally chosen, we show that the multiroute flow is a 2-approximation algorithm for most of randomly generated graphs. Our experimental results show that our algorithm has 15%-37% better performance than max-flow algorithm.

Algorithms for finding robust and sustainable network flows against multilink-attack

This work improves algorithms for finding network flows both sustainable and robust against multilink-attack (MLA). It brings out the relationship between sustainability (flow solution before attack known as MLA-reliable flow) and robustness (flow value after attack known as MLA-robust flow). Both problems are known to be NP-hard. However, exact polynomial time algorithms exist for certain categories of network. It includes the Extended Multiroute Flow (EMRF) algorithm that exhibits a solution to both MLA-robust and MLA-reliable flows. The class of networks solved by EMRF is extended here by using a capacity differentiation method. Although, the previous best-known approximation algorithm to both problems is the naturally robust and sustainable multiroute flow algorithm. A deeper analysis of EMRF an MLA problems leads to new methods to find tighter upper and lower bounds. The success rate of EMRF and the quality of the approximation is evaluated on practical networks as complex networks or grids.

Semimetric Properties of Sørensen-Dice and Tversky Indexes

In this work we prove a semimetric property for distances used for finding dissimilarities between two finite sets such as the Sorensen-Dice and the Tversky indexes. The Jaccard-Tanimoto index is known to be one of the most common distances for the task. Because the distance is a metric, when used, several algorithms can be applied to retrieve information from the data. Although the Sorensen-Dice index is known to be more robust than the Jaccard-Tanimoto when some information is missing from datasets, the distance is not a metric as it does not satisfy the triangle inequality. Recently, there are several machine learning algorithms proposed which use non-metric distances. Hence, instead of the triangle inequality, it is required that the distance satisfies the approximate triangle inequality with some small value of \(\rho \). This motivates us to find the value of \(\rho \) for the Sorensen-Dice index. In this paper, we prove that this value is 1.5. Besides, we can find the value for some of the Tversky index.

Improving Motivation in Survey Participation by Question Reordering

We organized an experiment to show that survey participants take part more when the questionnaires started with less aggressive questions. In our earlier work, we used Bayesian probability and graph algorithms to find relative values of each personal attribute. Using that valuation, we created two sets of the questionnaire each differs in question order and ask 33 personal attributes from participants. The first set of the questionnaire ordered questions from personal attributes with high valuations such as passport number, driving license number, last name, and monthly income to personal attributes with low valuations such as nationality, gender and office country. On the other hand, the second set of questionnaire ordered from those with low valuations to those with higher valuations. As a result, the number of participants who received the second set of the questionnaire and agrees to submit some information is 71.42 % more than those who received the first set of the questionnaire. Moreover, the second set of participants spends much less time in filling the questionnaire, but provides 1.78 % more information on average. (Parts of contents in this paper is presented at the 3rd domestic meeting of JSAI Special Interest Group on Business Informatics (SIG-BI). Although the preprint version of this paper can be obtained at the conference website [15], the version is not refereed and not considered as a publication.)

Calculating average joint hamming weight for minimal weight conversion of d integers

In this paper, we propose an algorithm to calculate the efficiency of number representations in elliptic curve cryptography, average joint Hamming weight. The method uses Markov chains generated from a minimal weight conversion algorithm of d integers using the minimal weight conversion. With redundant representations using digit sets like {0, ±1}, it is possible to reduce computation time of the cryptosystem. Although larger digit sets make the computation time shorter, it requires longer preprocessing time. Therefore, the average joint Hamming weight is useful to evaluate digit sets. The Markov chains to find the average joint Hamming weight are derived automatically from the conversions. However, the number of states in these Markov chains is generally infinite. In [8], we propose an algorithm to reduce the number of states, but it is still unclear which representations the method can be applied for. In this paper, the finiteness of Markov chain with the existence of a stationary distribution is proven in a class of representation whose digit set DS be a finite set such that there exists a natural number Λ where DS ⊆{0, ±1, …, ±Λ} and {0,±1, ±Λ}⊆DS . The class covers most of the representation practically used in elliptic curve cryptography such as the representation which digit set are {0, ±1} and {0, ±1, ±3}.

Bilevel Model for Adaptive Network Flow Problem

Abstract We propose to solve the adaptive network flow problem via a bilevel optimization framework. In this problem, we aim to find a flow that is most robust against any k edges attack. There is an exact algorithm proposed to solve the problem in a specific class of input graphs. However, for some input graphs that are not in that class, a flow obtained from the algorithms is sometimes much less robust than the optimal one. That motivates us to find an efficient exact algorithm based on bilevel optimization framework for the problem in this paper. The framework can give us much better results using reasonable amount of times.

Reducing Recovery Error in Compressive Sensing with Limited Number of Base Stations

We aim to decrease a communication cost of a network that uses compressive sensing, a technique that allows us to recover global information of sparse data by using only a small set of samples. Despite efficiency of the technique, collecting information from all samples is usually costly. Because the samples from previous works usually spread around the network, setting up a number of base stations does not help reducing the cost. In this paper, we propose a method that can utilize the base stations, while aiming to minimize the recovery error of compressive sensing. Based on theorem by Xu et al., which is for cost-aware compressive sensing, we derive a mathematical program that aims to maximize the preciseness in the setting. Then, we approximate the program by a convex quadratic program and prove that the approximation ratio is 0.63. Our simulation results show that, by using the coverage, the sampling error is decreased by at most thirty times.