Related papers: Distance Closures on Complex Networks
We present improved deterministic algorithms for approximating shortest paths in the Congested Clique model of distributed computing. We obtain $poly(\log\log n)$-round algorithms for the following problems in unweighted undirected…
In weighted graphs the shortest path between two nodes is often reached through an indirect path, out of all possible connections, leading to structural redundancies which play key roles in the dynamics and evolution of complex networks. We…
In data analysis, there is a strong demand for graph metrics that differ from the classical shortest path and resistance distances. Recently, several new classes of graph metrics have been proposed. This paper presents some of them…
We study the decremental All-Pairs Shortest Paths (APSP) problem in undirected edge-weighted graphs. The input to the problem is an $n$-vertex $m$-edge graph $G$ with non-negative edge lengths, that undergoes a sequence of edge deletions.…
Despite persistent efforts, there is no known technique for obtaining unconditional super-linear lower bounds for the computational complexity of the problems in P. Vassilevska Williams and Williams introduce a fruitful approach to advance…
We describe the structure of connected graphs with the minimum and maximum average distance, radius, diameter, betweenness centrality, efficiency and resistance distance, given their order and size. We find tight bounds on these graph…
Consider a setting where possibly sensitive information sent over a path in a network is visible to every {neighbor} of the path, i.e., every neighbor of some node on the path, thus including the nodes on the path itself. The exposure of a…
We study the problem of releasing the weights of all-pair shortest paths in a weighted undirected graph with differential privacy (DP). In this setting, the underlying graph is fixed and two graphs are neighbors if their edge weights differ…
We address the problem of defining a network graph on a large collection of classes. Each class is comprised of a collection of data points, sampled in a non i.i.d. way, from some unknown underlying distribution. The application we consider…
We introduce the tree distance, a new distance measure on graphs. The tree distance can be computed in polynomial time with standard methods from convex optimization. It is based on the notion of fractional isomorphism, a characterization…
We revisit the problem of privately releasing the all-pairs shortest path distances of a weighted undirected graph up to low additive error, which was first studied by Sealfon [Sea16]. In this paper, we improve significantly on Sealfon's…
From longitudinal biomedical studies to social networks, graphs have emerged as a powerful framework for describing evolving interactions between agents in complex systems. In such studies, after pre-processing, the data can be represented…
We study the reverse shortest path problem on disk graphs in the plane. In this problem we consider the proximity graph of a set of $n$ disks in the plane of arbitrary radii: In this graph two disks are connected if the distance between…
We present a new deterministic algorithm for distributed weighted all pairs shortest paths (APSP) in both undirected and directed graphs. Our algorithm runs in $\tilde{O}(n^{4/3})$ rounds in the Congest models on graphs with arbitrary edge…
We study two popular ways to sketch the shortest path distances of an input graph. The first is distance preservers, which are sparse subgraphs that agree with the distances of the original graph on a given set of demand pairs. Prior work…
Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…
We describe the structure of the graphs with the smallest average distance and the largest average clustering given their order and size. There is usually a unique graph with the largest average clustering, which at the same time has the…
In this paper we are interested in a version of the All-pairs Shortest Paths problem (APSP) that fits neither in the exact nor in the approximate case. We define a measure of centrality of a shortest path, related to the ``importance'' of…
Evaluating graphs learned by causal discovery algorithms is difficult: The number of edges that differ between two graphs does not reflect how the graphs differ with respect to the identifying formulas they suggest for causal effects. We…
The graph isomorphism, subgraph isomorphism, and graph edit distance problems are combinatorial problems with many applications. Heuristic exact and approximate algorithms for each of these problems have been developed for different kinds…