Related papers: Weighted paths between partitions
Studying the generalized Hamming weights of linear codes is a significant research area within coding theory, as it provides valuable structural information about the codes and plays a crucial role in determining their performance in…
We present a permutation-invariant distance between atomic configurations, defined through a functional representation of atomic positions. This distance enables to directly compare different atomic environments with an arbitrary number of…
The degree centrality of a node, defined as the number of nodes adjacent to it, is often used as a measure of importance of a node to the structure of a network. This metric can be extended to paths in a network, where the degree centrality…
We provide an implementation to compute the flat metric in any dimension. The flat metric, also called dual bounded Lipschitz distance, generalizes the well-known Wasserstein distance $W_1$ to the case that the distributions are of unequal…
We present results on the enumeration of crossings and nestings for matchings and set partitions. Using a bijection between partitions and vacillating tableaux, we show that if we fix the sets of minimal block elements and maximal block…
When reasoning about tasks that involve large amounts of data, a common approach is to represent data items as objects in the Hamming space where operations can be done efficiently and effectively. Object similarity can then be computed by…
We present a novel feasibility criteria for the finite intersection of convex sets given by inequalities. This criteria allows us to easily assert the feasibility by analyzing the unconstrained minimum of a speci?fic convex function, that…
We study distributed protocols for finding all pairs of similar vectors in a large dataset. Our results pertain to a variety of discrete metrics, and we give concrete instantiations for Hamming distance. In particular, we give improved…
A heavy path in a weighted graph represents a notion of connectivity and ordering that goes beyond two nodes. The heaviest path of length l in the graph, simply means a sequence of nodes with edges between them, such that the sum of edge…
In several multiobjective decision problems Pairwise Comparison Matrices (PCM) are applied to evaluate the decision variants. The problem that arises very often is the inconsistency of a given PCM. In such a situation it is important to…
Knowing which parts of a complex system have identical roles simplifies computations and reveals patterns in its network structure. Group theory has been applied to study symmetries in unweighted networks. However, in real-world weighted…
Minimum Label Cut (or Hedge Connectivity) problem is defined as follows: given an undirected graph $G=(V, E)$ with $n$ vertices and $m$ edges, in which, each edge is labeled (with one or multiple labels) from a label set $L=\{\ell_1,\ell_2,…
We introduce a principled way of computing the Wasserstein distance between two distributions in a federated manner. Namely, we show how to estimate the Wasserstein distance between two samples stored and kept on different devices/clients…
We first consider interval partitions whose complements are Lebesgue-null and introduce a complete metric that induces the same topology as the Hausdorff distance (between complements). This is done using correspondences between intervals.…
The quantale of distance distributions is of fundamental importance for understanding probabilistic metric spaces as enriched categories. Motivated by the categorical interpretation of partial metric spaces, we are led to investigate the…
Consider a graph with a set of vertices and oriented edges connecting pairs of vertices. Each vertex is associated with a random variable and these are assumed to be independent. In this setting, suppose we wish to solve the following…
This paper revisits the ordered statistics decoding (OSD). It provides a comprehensive analysis of the OSD algorithm by characterizing the statistical properties, evolution and the distribution of the Hamming distance and weighted Hamming…
A statistically principled way of conducting weighted network analysis is still lacking. Comparison of different populations of weighted networks is hard because topology is inherently dependent on wiring cost, where cost is defined as the…
We address the problem of computing distances between rankings that take into account similarities between candidates. The need for evaluating such distances is governed by applications as diverse as rank aggregation, bioinformatics, social…
Continuous 2-dimensional space is often discretized by considering a mesh of weighted cells. In this work we study how well a weighted mesh approximates the space, with respect to shortest paths. We consider a shortest path $…