We study the minimum diameter color-spanning set problem which has recently drawn some attention in the database community. We show that the problem can be solved in polynomial time for L1 and L∞ metrics, while it is NP-hard for all other Lp metrics even in two dimensions. However, we can efficiently compute a constant factor approximation.

Learning vector quantization applying non-standard metrics became quite popular for classification performance improvement compared to standard approaches using the Euclidean distance. Kernel metrics and quadratic forms belong to the most promising approaches. In this paper we consider Minkowski distances (lp-norms). In particular, l1-norms are known to be robust against noise in data, such tha...

in this paper, we study a class of finsler metrics which contains the class of p-reducible andgeneral relatively isotropic landsberg metrics, as special cases. we prove that on a compact finsler manifold,this class of metrics is nothing other than randers metrics. finally, we study this class of finsler metrics withscalar flag curvature and find a condition under which these metrics reduce to r...

This paper develops a new integrated ball (pseudo)metric which provides an intermediary between chosen starting d and the Lp distance in general function spaces. Selecting as Hausdorff or Fréchet distances, we introduce shape-sensitive versions of these supremum-based metrics. The metrics allow for finer analyses functional settings, not attainable applying non-integrated directly. Moreover, co...

One of the primary concerns in any system design problem is to prepare a highly reliable system with minimum cost. One way to increase the reliability of systems is to use redundancy in different forms such as active or standby. In this paper, a new nonlinear multi- objective integer programming model with the choice of redundancy strategy and component type is developed where standby strategy ...

We introduce the Bipartite Multi-cut problem. This is a generalization of the st-Min-cut problem, is similar to the Multi-cut problem (except for more stringent requirements) and also turns out to be an immediate generalization of the Min UnCut problem. We prove that this problem is NP-hard and then present LP and SDP based approximation algorithms. While the LP algorithm is based on the Garg-V...

Measuring the transmitted information in metric-based clustering has become something of a standard test for the performance of a spike train metric. In this comment, the recently proposed Lp VictorPurpura metric is used to cluster spiking responses to zebra finch songs, recorded from field L of anesthetized zebra finch. It is found that for these data the Lp metrics with p > 1 modestly outperf...

Measuring the transmitted information in metric-based clustering has become something of a standard test for the performance of a spike train metric. In this comment, the recently proposed Lp VictorPurpura metric is used to cluster spiking responses to zebra finch songs, recorded from field L of anesthetized zebra finch. It is found that for these data the Lp metrics with p > 1 modestly outperf...

Invented in the 1960’s, permutation codes have reemerged in recent years as a topic of great interest because of properties making them attractive for certain modern technological applications. In 2011 a decoding method called LP (linear programming) decoding was introduced for a class of permutation codes with a Euclidean distance induced metric. In this paper we comparatively analyze the Eucl...

Products of independent identically distributed random stochastic 2 × 2 matrices are known to converge in distribution under a trivial condition. Rates for this convergence are estimated in terms of the minimal Lp-metrics and the Kolmogorov metric and applications to convergence rates of related interval splitting procedures are discussed. AMS subject classifications. Primary: 60F05; secondary:...