Naoki Katoh

Bio: Naoki Katoh is an academic researcher from University of Hyogo. The author has contributed to research in topics: Time complexity & Vertex (geometry). The author has an hindex of 31, co-authored 268 publications receiving 4707 citations. Previous affiliations of Naoki Katoh include Kyoto University & Kobe University.

Resource Allocation Problems: Algorithmic Approaches

Abstract: (1989). Resource Allocation Problems: Algorithmic Approaches. Journal of the Operational Research Society: Vol. 40, No. 7, pp. 701-702.

Applications of weighted Voronoi diagrams and randomization to variance-based k-clustering: (extended abstract)

Abstract: In this paper we consider thek-clustering problem for a set S of n points i=(xi) in thed-dimensional space with variance-based errors as clustering criteria, motivated from the color quantization problem of computing a color lookup table for frame buffer display. As the inter-cluster criterion to minimize, the sum on intra-cluster errors over every cluster is used, and as the intra-cluster criterion of a cluster Sj,|Sj|α-1 ΣpiϵSj || xi - x(Sj)||2is considered, where ||·|| is the L2 norm and x(Sj) is the centroid of points in Sj, i.e., (1/|Sj|)Σp ∈Sjxi. The cases of α=1,2 correspond to the sum of squared errors and the all-pairs sum of squared errors, respectively.The k-clustering problem under the criterion with α=1,2 are treated in a unified manner by characterizing the optimum solution to the kclustering problem by the ordinary Euclidean Voronoi diagram and the weighted Voronoi diagram with both multiplicative and additive weights. With this framework, the problem is related to the generalized primary shutter function for the Voronoi diagrams. The primary shutter function is shown to be O(nO(kd)), which implies that, for fixed k, this clustering problem can be solved in a polynomial time. For the problem with the most typical intra-cluster criterion of the sum of squared errors, we also present an efficient randomized algorithm which, roughly speaking, finds an ∈–approximate 2–clustering in O(n(1/∈)d) time, which is quite practical and may be used to real large-scale problems such as the color quantization problem.

Resource Allocation Problems

Abstract: The resource allocation problem seeks to find an optimal allocation of a fixed amount of resources to activities so as to minimize the cost incurred by the allocation. A simplest form of the problem is to minimize a separable convex function under a single constraint concerning the total amount of resources to be allocated. The amount of resources to be allocated to each activity is treated as a continuous or integer variable, depending on the cases. This can be viewed as a special case of the nonlinear programming problem or the nonlinear integer programming problem.

An efficient algorithm for K shortest simple paths

Abstract: This article gives an efficient algorithm for obtaining K shortest simple paths between two specified nodes in an undirected graph G with non-negative edge lengths. Letting n be the number of nodes and m be the number of edges in G, its running time is O(Kc(n, m)) if the shortest paths from one node to all the other nodes are obtained in c(n, m) [≥O(m)] time, and the required space is O(Kn + m). This time bound is better than those realized by existing algorithms, the best of which, proposed by Yen, requires O(Kn3) time, since c(n, m) ≤min[O(n2), O(m log n)] is known.

k-means++: the advantages of careful seeding

Abstract: The k-means method is a widely used clustering technique that seeks to minimize the average squared distance between points in the same cluster. Although it offers no accuracy guarantees, its simplicity and speed are very appealing in practice. By augmenting k-means with a very simple, randomized seeding technique, we obtain an algorithm that is Θ(logk)-competitive with the optimal clustering. Preliminary experiments show that our augmentation improves both the speed and the accuracy of k-means, often quite dramatically.

Evolutionary algorithms for solving multi-objective problems

Abstract: List of Figures. List of Tables. Preface. Foreword. 1. Basic Concepts. 2. Evolutionary Algorithm MOP Approaches. 3. MOEA Test Suites. 4. MOEA Testing and Analysis. 5. MOEA Theory and Issues. 3. MOEA Theoretical Issues. 6. Applications. 7. MOEA Parallelization. 8. Multi-Criteria Decision Making. 9. Special Topics. 10. Epilog. Appendix A: MOEA Classification and Technique Analysis. Appendix B: MOPs in the Literature. Appendix C: Ptrue & PFtrue for Selected Numeric MOPs. Appendix D: Ptrue & PFtrue for Side-Constrained MOPs. Appendix E: MOEA Software Availability. Appendix F: MOEA-Related Information. Index. References.

Marketing for management.

Abstract: MKT 6009 Marketing Internship (0 semester credit hours) Student gains experience and improves skills through appropriate developmental work assignments in a real business environment. Student must identify and submit specific business learning objectives at the beginning of the semester. The student must demonstrate exposure to the managerial perspective via involvement or observation. At semester end, student prepares an oral or poster presentation, or a written paper reflecting on the work experience. Student performance is evaluated by the work supervisor. Pass/Fail only. Prerequisites: (MAS 6102 or MBA major) and department consent required. (0-0) S MKT 6244 Digital Marketing Strategy (2 semester credit hours) Executive Education Course. The course explores three distinct areas within marketing and sales namely, digital marketing, traditional sales prospecting, and executive sales organization and strategy. The continuing convergence of the digital marketing and sales funnels has created a strategic continuum from digital lead generation to digital sales. The course identifies the current composition of this digital continuum while providing opportunities to evaluate sales and marketing digital strategies. Prerequisites: MKT 6301 and instructor consent required. (2-0) Y MKT 6301 (SYSM 6318) Marketing Management (3 semester credit hours) Overview of marketing management methods, principles and concepts including product, pricing, promotion and distribution decisions as well as segmentation, targeting and positioning. (3-0) S MKT 6309 Marketing Data Analysis and Research (3 semester credit hours) Methods employed in market research and data analysis to understand consumer behavior, customer journeys, and markets so as to enable better decision-making. Topics include understanding different sources of data, survey design, experiments, and sampling plans. The course will cover the techniques used for market sizing estimation and forecasting. In addition, the course will cover the foundational concepts and techniques used in data visualization and \"story-telling\" for clients and management. Corequisites: MKT 6301 and OPRE 6301. (3-0) Y MKT 6310 Consumer Behavior (3 semester credit hours) An exposition of the theoretical perspectives of consumer behavior along with practical marketing implication. Study of psychological, sociological and behavioral findings and frameworks with reference to consumer decision-making. Topics will include the consumer decision-making model, individual determinants of consumer behavior and environmental influences on consumer behavior and their impact on marketing. Prerequisite: MKT 6301. (3-0) Y MKT 6321 Interactive and Digital Marketing (3 semester credit hours) Introduction to the theory and practice of interactive and digital marketing. Topics covered include: online-market research, consumer behavior, conversion metrics, and segmentation considerations; ecommerce, search and display advertising, audiences, search engine marketing, email, mobile, video, social networks, and the Internet of Things. (3-0) T MKT 6322 Internet Business Models (3 semester credit hours) Topics to be covered are: consumer behavior on the Internet, advertising on the Internet, competitive strategies, market research using the Internet, brand management, managing distribution and supply chains, pricing strategies, electronic payment systems, and developing virtual organizations. Further, students learn auction theory, web content design, and clickstream analysis. Prerequisite: MKT 6301. (3-0) Y MKT 6323 Database Marketing (3 semester credit hours) Techniques to analyze, interpret, and utilize marketing databases of customers to identify a firm's best customers, understanding their needs, and targeting communications and promotions to retain such customers. Topics

An efficient k-means clustering algorithm: analysis and implementation

Abstract: In k-means clustering, we are given a set of n data points in d-dimensional space R/sup d/ and an integer k and the problem is to determine a set of k points in Rd, called centers, so as to minimize the mean squared distance from each data point to its nearest center. A popular heuristic for k-means clustering is Lloyd's (1982) algorithm. We present a simple and efficient implementation of Lloyd's k-means clustering algorithm, which we call the filtering algorithm. This algorithm is easy to implement, requiring a kd-tree as the only major data structure. We establish the practical efficiency of the filtering algorithm in two ways. First, we present a data-sensitive analysis of the algorithm's running time, which shows that the algorithm runs faster as the separation between clusters increases. Second, we present a number of empirical studies both on synthetically generated data and on real data sets from applications in color quantization, data compression, and image segmentation.