相关论文: Global sum on symmetric networks
Motivated by applications in machine learning and statistics, we study distributed optimization problems over a network of processors, where the goal is to optimize a global objective composed of a sum of local functions. In these problems,…
It is not difficult to think of applications that can be modelled as graph problems in which placing some facility or commodity at a vertex has some positive or negative effect on the values of all the vertices out to some distance, and we…
We consider the problem of communicating the sum of $m$ sources to $n$ terminals in a directed acyclic network. Recently, it was shown that for a network of unit capacity links with either $m=2$ or $n=2$, the sum of the sources can be…
Sampling is a fundamental topic in graph signal processing, having found applications in estimation, clustering, and video compression. In contrast to traditional signal processing, the irregularity of the signal domain makes selecting a…
We answer a question about the diameter of an order-super-commuting graph on a symmetric group by studying the number-theoretical concept of $d$-complete sequences of primes in arithmetic progression.
We announce two breakthrough results concerning important questions in the Theory of Computational Complexity. In this expository paper, a systematic and comprehensive geometric characterization of the Subset Sum Problem is presented. We…
A variety of network modeling problems begin by generating a degree sequence drawn from a given probability distribution. If the randomly generated sequence is not graphic, we give a new approach for generating a graphic approximation of…
The diameter of a graph is the maximum distance among all pairs of vertices. Thus a graph $G$ has diameter $d$ if any two vertices are at distance at most $d$ and there are two vertices at distance $d$. We are interested in studying the…
In this paper we offer a metric similar to graph edit distance which measures the distance between two (possibly infinite)weighted graphs with finite norm (we define the norm of a graph as the sum of absolute values of its edges). The main…
We study the Minimum Sum Vertex Cover problem, which asks for an ordering of vertices in a graph that minimizes the total cover time of edges. In particular, n vertices of the graph are visited according to an ordering, and for each edge…
Finding all maximal $k$-plexes on networks is a fundamental research problem in graph analysis due to many important applications, such as community detection, biological graph analysis, and so on. A $k$-plex is a subgraph in which every…
The Straightness is a measure designed to characterize a pair of vertices in a spatial graph. It is defined as the ratio of the Euclidean distance to the graph distance between these vertices. It is often used as an average, for instance to…
The study of the graph diameter of polytopes is a classical open problem in polyhedral geometry and the theory of linear optimization. In this paper we continue the investigation initiated in [4] by introducing a vast hierarchy of…
On the Euclidean domains of classical signal processing, linking of signal samples to the underlying coordinate structure is straightforward. While graph adjacency matrices totally define the quantitative associations among the underlying…
Current methods of graph signal processing rely heavily on the specific structure of the underlying network: the shift operator and the graph Fourier transform are both derived directly from a specific graph. In many cases, the network is…
We define direct sums and a corresponding notion of connectedness for graph limits. Every graph limit has a unique decomposition as a direct sum of connected components. As is well-known, graph limits may be represented by symmetric…
Quantifying the similarity between two graphs is a fundamental algorithmic problem at the heart of many data analysis tasks for graph-based data. In this paper, we study the computational complexity of a family of similarity measures based…
We study a simple random process in which vertices of a connected graph reach consensus through pairwise interactions. We compute outcome probabilities, which do not depend on the graph structure, and consider the expected time until a…
Centrality describes the importance of nodes in a graph and is modeled by various measures. Its global analogue, called centralization, is a general formula for calculating a graph-level centrality score based on the node-level centrality…
In this paper, we introduce a new concept namely degree polynomial for vertices of a simple graph. This notion leads to a concept namely degree polynomial sequence which is stronger than the concept of degree sequence. After obtaining the…