Sanpawat Kantabutra

Survey of Clustering: Algorithms and Applications

This article is a survey into clustering applications and algorithms. A number of important well-known clustering methods are discussed. The authors present a brief history of the development of the field of clustering, discuss various types of clustering, and mention some of the current research directions in the field of clustering. More specifically, top-down and bottom-up hierarchical clustering are described. Additionally, K-Means and K-Medians clustering algorithms are also shown. The concept of representative points is introduced and the technique of discovering them is presented. Immense data sets in clustering often necessitate parallel computation. The authors discuss issues involving parallel clustering as well. Clustering deals with a large number of experimental results. The authors provide references to these works throughout the article. A table for comparing various clustering methods is given in the end. The authors give a summary and an extensive list of references, including some of the latest works in the field, to conclude the article.

A mobility model for studying wireless communication and the complexity of problems in the model

Wireless communication has become omnipresent in the world and enables users to have an unprecedented ability to communicate any time and any place. In this article, we propose a mobility model for studying wireless communication. The model incorporates elements such as users, access points, and obstacles so that it faithfully mimics the real environment. Interesting problems that have practical applications are posed and solved. More specifically, we study the complexity of three problems in a grid. The source reachability problem (SRP) models a situation in which we want to determine whether two access points can communicate at a certain time in a mobile environment. When users are involved in this situation, we call this problem the user communication problem (UCP). We show that SRP can be solved in O(max{d,t}m2) time, where d is the number of obstacles, t is the time bound in the statement of the problem, and m is the number of access points; we show that UCP can be solved in O(max{d,t}m4) time. The third problem called the user communication, limited source access problem (UCLSAP) studies a situation where we want to determine whether two users can communicate uninterruptedly during the duration of the model while considering battery-time limits of the access points. In contrast to the first two problems, we demonstrate that UCLSAP is intractable, unless P = NP. In conclusion, we briefly discuss the extension of our model to three dimensions and provide a list of open problems.

Under-sampling by algorithm with performance guaranteed for class-imbalance problem

Class-imbalance problem is the problem that the number, or data, in the majority class is much more than in the minority class. Traditional classifiers cannot sort out this problem because they focus on the data in the majority class than on the data in the minority class, and then they predict some upcoming data as the data in the majority class. Under-sampling is an efficient way to handle this problem because this method selects the representatives of the data in the majority class. For this reason, under-sampling occupies shorter training period than over-sampling. The only problem with the under-sampling method is that a representative selection, in all probability, throws away important information in a majority class. To overcome this problem, we propose a cluster-based under-sampling method. We use a clustering algorithm that is performance guaranteed, named k-centers algorithm, which clusters the data in the majority class and selects a number of representative data in many proportions, and then combines them with all the data in the minority class as a training set. In this paper, we compare our approach with k-means on five datasets from UCI with two classifiers: 5-nearest neighbors and c4.5 decision tree. The performance is measured by Precision, Recall, F-measure, and Accuracy. The experimental results show that our approach has higher measurements than the k-means approach, except Precision where both the approaches have the same rate.

The graph relabeling problem and its variants

Graph labeling is a classic problem in mathematics and computing. In this paper we study an interesting set of graph labeling problems which were first introduced by Kantabutra (2007). The general problem, here called the graph relabeling problem, is to take an undirected graph G=(V, E), two labelings l1 and l2 of G, and a label switching function f and then to determine the complexity of transforming the labeling l1 into l2 using f. We define several variants of the problem and discuss their complexity. We give tight bounds for one version of the problem on chains, and show another version is NP-complete. These problems have applications in areas such as bioinformatics, networks, and VLSI.

Time-optimal user communication and source reachability algorithms in a two-dimensional grid wireless mobility model

This paper describes a communication model in a two-dimensional grid for mobile wireless networks and shows how to optimally solve some decision problems related to the model. We show that user communication problem (UCP) and source reachability problem (SRP) can be most efficiently solved in polynomial time. Asymptotically time-optimal algorithms for solving these problems are also presented.

The parallel complexities of the k-medians related problems

K-medians is a well-known clustering algorithm in data mining literature. This paper describes three decision problems related to k-medians. These problems are called medians replacement in k-medians, median determination, and T iterations k-medians problems. We show that these problems are in NC, each has a (logn)O(1) parallel time algorithm on an EREW PRAM model using nO(1) processors, and the result in each case is the strongest possible.

It’s elementary, my dear watson: time-optimal sorting algorithms on a completely overlapping network

Several parallel architectures exist in computer science literature. Motivated by the experimental overlapping connectivity network, we propose a new theoretical network called a completely overlapping network (CON). This network is an extension of the overlapping connectivity network with multiple buses. In this paper we investigate some properties of this network and demonstrate the use of CON and its usefulness by solving two toy problems: decimal number and one-digit binary number sortings.

The Structure of Rooted Weighted Trees Modeling Layered Cyber-security Systems

In this paper we consider the structure and topology of a layered-security model in which the containers and their nestings are given in the form of a rooted tree T. A cyber-security model is an ordered three-tuple M = (T, C, P) where C and P are multisets of penetration costs for the containers and target-acquisition values for the prizes that are located within the containers, respectively, both of the same cardinality as the set of the non-root vertices of T. The problem that we study is to assign the penetration costs to the edges and the target-acquisition values to the vertices of the tree T in such a way that minimizes the total prize that an attacker can acquire given a limited budget. The attacker breaks into containers starting at the root of T and once a vertex has been broken into, its children can be broken into by paying the associated penetration costs. The attacker must deduct the corresponding penetration cost from the budget, as each new container is broken into. For a given assignment of costs and target values we obtain a security system. We show that in general it is not possible to develop an optimal security system for a given cyber-security model M. We define P- and C-models where the penetration costs and prizes, respectively, all have unit value. We show that if T is a rooted tree such that any P- or C-model M = (T, C, P) has an optimal security system, then T is one of the following types: (i) a rooted path, (ii) a rooted star, (iii) a rooted 3-caterpillar, or (iv) a rooted 4-spider. Conversely, if T is one of these four types of trees, then we show that any P- or C-model M = (T, C, P) does have an optimal security system. Finally, we study a duality between P- and C-models that allows us to translate results for P-models into corresponding results for C-models and vice versa. The results obtained give us some mathematical insights into how layered-security defenses should be organized.

On the parallel complexity of minimum sum of diameters clustering

Given a set of n entities to be classified, and a matric of dissimilarities between pairs of them. This paper considers the problem called Minimum Sum of Diameters Clustering Problem, where a partition of the set of entities into k clusters such that the sum of the diameters of these clusters is minimized. Brucker showed that the complexity of the problem is NP-hard, when k ≥ 3 [1]. For the case of k = 2, Hansen and Jaumard gave an O(n3 log n) algorithm [2], which Ramnath later improved the running time to O(n3) [3]. This paper discusses the parallel complexity of the Minimum Sum of Diameters Clustering Problem. For the case of k = 2, we show that the problem in parallel in fact belongs in class NC1 In particular, we show that the parallel complexity of the problem is O(log n) parallel time and n7 processors on the Common CRCW PRAM model. Additionally, we propose the parallel algorithmic technique which can be applied to improve the processor bound by a factor of n. As a result, we show that the problem can be quickly solved in O(log n) parallel time using n6 processors on the Common CRCW PRAM model. In addition, regarding the issue of high processor complexity, we also propose a more practical NC algorithm which can be implemented in O(log3 n) parallel time using n3.376 processors on the EREW PRAM model.

The complexity of the overlay network verification and its related problems

In this paper we introduce a special type of virtual networks called an overlay network. We first study a decision problem called the Overlay Network Verification Problem and show that this problem is NP-complete. We then place some restriction to the original problem and prove that the Overlay Network Verification Problem still remains NP-complete. A similar problem called the Two-Label Overlay Network Verification Problem is then investigated. The complexities of this problem and its variant are then discussed. A list of open problems and the real-world applications of our results are given in the conclusion.