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We consider the problem of finding a minimum edge cost subgraph of a graph satisfying both given node-connectivity requirements and degree upper bounds on nodes. We present an iterative rounding algorithm of the biset LP relaxation for this…
In Path Set Packing, the input is an undirected graph $G$, a collection $\calp$ of simple paths in $G$, and a positive integer $k$. The problem is to decide whether there exist $k$ edge-disjoint paths in $\calp$. We study the parameterized…
Given two $k$-graphs $H$ and $F$, a perfect $F$-packing in $H$ is a collection of vertex-disjoint copies of $F$ in $H$ which together cover all the vertices in $H$. In the case when $F$ is a single edge, a perfect $F$-packing is simply a…
Given a bipartite graph $G$, the \textsc{Bicluster Editing} problem asks for the minimum number of edges to insert or delete in $G$ so that every connected component is a bicluster, i.e. a complete bipartite graph. This has several…
Partitioning a graph into blocks of "roughly equal" weight while cutting only few edges is a fundamental problem in computer science with a wide range of applications. In particular, the problem is a building block in applications that…
Discovering dense subgraphs and understanding the relations among them is a fundamental problem in graph mining. We want to not only identify dense subgraphs, but also build a hierarchy among them (e.g., larger but sparser subgraphs formed…
The problem of identifying the maximum edge biclique in bipartite graphs has attracted considerable attention in bipartite graph analysis, with numerous real-world applications such as fraud detection, community detection, and online…
We consider the following problem for a fixed graph H: given a graph G and two H-colorings of G, i.e. homomorphisms from G to H, can one be transformed (reconfigured) into the other by changing one color at a time, maintaining an H-coloring…
In the k-arc connected subgraph problem, we are given a directed graph G and an integer k and the goal is the find a subgraph of minimum cost such that there are at least k-arc disjoint paths between any pair of vertices. We give a simple…
The notion of degree-constrained spanning hierarchies, also called k-trails, was recently introduced in the context of network routing problems. They describe graphs that are homomorphic images of connected graphs of degree at most k. First…
The fair $k$-median problem is one of the important clustering problems. The current best approximation ratio is 4.675 for this problem with 1-fair violation, which was proposed by Bercea et al. [APPROX-RANDOM'2019]. As far as we know,…
Given a graph, the general problem to cover the maximum number of vertices by a collection of vertex-disjoint long paths seemingly escapes from the literature. A path containing at least $k$ vertices is considered long. When $k \le 3$, the…
The quantum query complexity of subgraph-containment problems, which ask whether a given subgraph $H$ is present in an input graph $G$, has been the subject of considerable study. However, even for relatively simple subgraphs, such as paths…
In the $k$-Edge Connected Spanning Subgraph ($k$-ECSS) problem we are given a (multi-)graph $G=(V,E)$ with edge costs and an integer $k$, and seek a min-cost $k$-edge-connected spanning subgraph of $G$. The problem admits a…
In the multiway cut problem, we are given an undirected graph with non-negative edge weights and a collection of $k$ terminal nodes, and the goal is to partition the node set of the graph into $k$ non-empty parts each containing exactly one…
We consider the classical $k$-means clustering problem in the setting bi-criteria approximation, in which an algoithm is allowed to output $\beta k > k$ clusters, and must produce a clustering with cost at most $\alpha$ times the to the…
The analysis of several algorithms and data structures can be framed as a peeling process on a random hypergraph: vertices with degree less than k are removed until there are no vertices of degree less than k left. The remaining hypergraph…
Bhawalkar, Kleinberg, Lewi, Roughgarden, and Sharma [ICALP 2012] introduced the Anchored k-Core problem, where the task is for a given graph G and integers b, k, and p to find an induced subgraph H with at least p vertices (the core) such…
We develop a novel parallel decomposition strategy for unweighted, undirected graphs, based on growing disjoint connected clusters from batches of centers progressively selected from yet uncovered nodes. With respect to similar previous…
A number of inference problems with sensor networks involve projecting a measured signal onto a given subspace. In existing decentralized approaches, sensors communicate with their local neighbors to obtain a sequence of iterates that…