Related papers: Approximation Algorithms for Probabilistic Graphs
In many physical, statistical, biological and other investigations it is desirable to approximate a system of points by objects of lower dimension and/or complexity. For this purpose, Karl Pearson invented principal component analysis in…
Many problems in computational geometry are not stated in graph-theoretic terms, but can be solved efficiently by constructing an auxiliary graph and performing a graph-theoretic algorithm on it. Often, the efficiency of the algorithm…
Nearest neighbor search and k-nearest neighbor graph construction are two fundamental issues arise from many disciplines such as multimedia information retrieval, data-mining and machine learning. They become more and more imminent given…
We present a novel approximation algorithm for $k$-median that achieves an approximation guarantee of $1+\sqrt{3}+\epsilon$, improving upon the decade-old ratio of $3+\epsilon$. Our approach is based on two components, each of which, we…
Finding dense subgraphs in a graph is a fundamental graph mining task, with applications in several fields. Algorithms for identifying dense subgraphs are used in biology, in finance, in spam detection, etc. Standard formulations of this…
We introduce and study the problem of balanced districting, where given an undirected graph with vertices carrying two types of weights (different population, resource types, etc) the goal is to maximize the total weights covered in vertex…
In the Densest k-Subgraph problem, given a graph G and a parameter k, one needs to find a subgraph of G induced on k vertices that contains the largest number of edges. There is a significant gap between the best known upper and lower…
Existing approaches to solving combinatorial optimization problems on graphs suffer from the need to engineer each problem algorithmically, with practical problems recurring in many instances. The practical side of theoretical computer…
Similarity graphs are an active research direction for the nearest neighbor search (NNS) problem. New algorithms for similarity graph construction are continuously being proposed and analyzed by both theoreticians and practitioners.…
We present KADABRA, a new algorithm to approximate betweenness centrality in directed and undirected graphs, which significantly outperforms all previous approaches on real-world complex networks. The efficiency of the new algorithm relies…
We study the problem of deleting a minimum cost set of vertices from a given vertex-weighted graph in such a way that the resulting graph has no induced path on three vertices. This problem is often called cluster vertex deletion in the…
The k-means objective is arguably the most widely-used cost function for modeling clustering tasks in a metric space. In practice and historically, k-means is thought of in a continuous setting, namely where the centers can be located…
In this work, we study the socially fair $k$-median/$k$-means problem. We are given a set of points $P$ in a metric space $\mathcal{X}$ with a distance function $d(.,.)$. There are $\ell$ groups: $P_1,\dotsc,P_{\ell} \subseteq P$. We are…
We consider the densest $k$-subgraph problem, which seeks to identify the $k$-node subgraph of a given input graph with maximum number of edges. This problem is well-known to be NP-hard, by reduction to the maximum clique problem. We…
Interval and proper interval graphs are very well-known graph classes, for which there is a wide literature. As a consequence, some generalizations of interval graphs have been proposed, in which graphs in general are expressed in terms of…
We present a $(1+\frac{k}{k+2})$-approximation algorithm for the Maximum $k$-dependent Set problem on bipartite graphs for any $k\ge1$. For a graph with $n$ vertices and $m$ edges, the algorithm runs in $O(k m \sqrt{n})$ time and improves…
The $k$-means algorithm is one of the most widely used clustering heuristics. Despite its simplicity, analyzing its running time and quality of approximation is surprisingly difficult and can lead to deep insights that can be used to…
We reformulate the Cavity Approximation (CA), a class of algorithms recently introduced for improving the Bethe approximation estimates of marginals in graphical models. In our new formulation, which allows for the treatment of multivalued…
Finding coarse representations of large graphs is an important computational problem in the fields of scientific computing, large scale graph partitioning, and the reduction of geometric meshes. Of particular interest in all of these fields…
In network analysis and graph mining, closeness centrality is a popular measure to infer the importance of a vertex. Computing closeness efficiently for individual vertices received considerable attention. The NP-hard problem of group…