Algorithmic Aspects in Information and Management: 11th by Riccardo Dondi, Guillaume Fertin, Giancarlo Mauri PDF

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By Riccardo Dondi, Guillaume Fertin, Giancarlo Mauri

ISBN-10: 3319411675

ISBN-13: 9783319411675

ISBN-10: 3319411683

ISBN-13: 9783319411682

This quantity constitutes the court cases of the eleventh foreign convention on Algorithmic features in info and administration, AAIM 2016, held in Bergamo, Italy, in July 2016.

The 18 revised complete papers awarded have been conscientiously reviewed and chosen from forty-one submissions. The papers take care of present developments of analysis on algorithms, info constructions, operation learn, combinatorial optimization and their applications.

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LNCS, vol. 8546, pp. 299–311. Springer, Heidelberg (2014) 7. : On the metric properties of discrete space-filling curves. IEEE Trans. Image Process. 5(5), 794–797 (1996) 8. : Towards optimal locality in meshindexings. Discrete Appl. Math. it Abstract. , Ak } of a set of points assuming that every cluster size |Ai | belongs to a given set M of positive integers. e. when the points are simply rational values, for an arbitrary set M of size constraints, which extends to the 1 -norm an analogous procedure known for the 2 -norm.

Clustering consists in grouping a set of objects into subsets, called clusters, that are maximally homogeneous [5,8]. Partitional or hard clustering requires the subsets to be disjoint and non-empty, and in the usual geometric setting the similarity between objects is measured by distance between points representing the objects [15]. , Ak ) = i W (Ai ) = i x∈Ai x − μ(Ai ) 2 of all clusters, where μ(Ai ) is the sample mean of Ai and · is the Euclidean norm. This partitional clustering problem is difficult: when d is part of the instance the problem is NP-hard even if the number of clusters is fixed to k = 2 [1]; the same occurs for arbitrary k with fixed dimension d = 2 [7,16].

We recall that, in case of 2 -norm, the weight of a cluster A can be computed by relation W2 (A) = 1 |A| a−b 2 2 (1) (∗) where the sum is extended to all unordered pairs {a, b} of distinct elements in A. , Ak } such that |Ai | ∈ M for every i = 1, . . , k, is called M-clustering. 1 When M is not included in the instance, but fixed in advance, we call the problem M-RSC-d (with p -norm). In this work we study these problems in dimension d = 1, 2 assuming 1 and 2 -norm. 3 Dynamic Programming for RSC on the Line In this section we describe a polynomial-time algorithm for RSC-1 that works assuming either 1 or 2 -norm.

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Algorithmic Aspects in Information and Management: 11th International Conference, AAIM 2016, Bergamo, Italy, July 18-20, 2016, Proceedings by Riccardo Dondi, Guillaume Fertin, Giancarlo Mauri


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