Related papers: Metric Spaces with Expensive Distances

We present a new parallel model of computation suitable for spatial architectures, for which the energy used for communication heavily depends on the distance of the communicating processors. In our model, processors have locations on a…

Consider the continuum of points along the edges of a network, i.e., a connected, undirected graph with positive edge weights. We measure the distance between these points in terms of the weighted shortest path distance, called the network…

A method of induction the distances with Hilbert structure is proposed. Some properties of the method are studied. Typical examples of corresponding metric spaces are discussed. Key words: Hilbert spaces; metric spaces; isometric embedding…

The capacitated p-center problem requires to select p facilities from a set of candidates to service a number of customers, subject to facility capacity constraints, with the aim of minimizing the maximum distance between a customer and its…

Most Machine Learning (ML) methods, from clustering to classification, rely on a distance function to describe relationships between datapoints. For complex datasets it is hard to avoid making some arbitrary choices when defining a distance…

This article provides an overview on the statistical modeling of complex data as increasingly encountered in modern data analysis. It is argued that such data can often be described as elements of a metric space that satisfies certain…

In syntax-guided synthesis, one of the challenges is to reduce the enormous size of the search space. We observe that most search spaces are not just flat sets of programs, but can be endowed with a structure that we call an oriented…

Metric embeddings are central to metric theory and its applications. Here we consider embeddings of a different sort: maps from a set to subsets of a metric space so that distances between points are approximated by minimal distances…

Finding global optima in high-dimensional optimization problems is extremely challenging since the number of function evaluations required to sufficiently explore the search space increases exponentially with its dimensionality.…

We propose randomized subspace gradient methods for high-dimensional constrained optimization. While there have been similarly purposed studies on unconstrained optimization problems, there have been few on constrained optimization problems…

Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…

A time series is a sequence of data items; typical examples are videos, stock ticker data, or streams of temperature measurements. Quite some research has been devoted to comparing and indexing simple time series, i.e., time series where…

We consider the problem of model reduction of parametrized PDEs where the goal is to approximate any function belonging to the set of solutions at a reduced computational cost. For this, the bottom line of most strategies has so far been…

Approximate K Nearest Neighbor (AKNN) search in high-dimensional spaces is a critical yet challenging problem. In AKNN search, distance computation is the core task that dominates the runtime. Existing approaches typically use approximate…

Persistent homology allows us to create topological summaries of complex data. In order to analyse these statistically, we need to choose a topological summary and a relevant metric space in which this topological summary exists. While…

Perspective functions arise explicitly or implicitly in various forms in applied mathematics and in statistical data analysis. To date, no systematic strategy is available to solve the associated, typically nonsmooth, optimization problems.…

Rectangles are used to approximate objects, or sets of objects, in a plethora of applications, systems and index structures. Many tasks, such as nearest neighbor search and similarity ranking, require to decide if objects in one rectangle A…

Consider the task of locating an unknown target point using approximate distance queries: in each round, a reconstructor selects a query point and receives a noisy version of its distance to the target. This problem arises naturally in…

The distance metric plays an important role in nearest neighbor (NN) classification. Usually the Euclidean distance metric is assumed or a Mahalanobis distance metric is optimized to improve the NN performance. In this paper, we study the…

In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…