相关论文: Finding Subgraphs in Highly Dynamic Networks

We study the problem of optimal leader selection in consensus networks with noisy relative information. The objective is to identify the set of $k$ leaders that minimizes the formation's deviation from the desired trajectory established by…

In a seminal work, Chiba and Nishizeki [SIAM J. Comput. `85] developed subgraph listing algorithms for triangles, 4-cycle and $k$-cliques, where $k \geq 3.$ The runtimes of their algorithms are parameterized by the number of edges $m$ and…

Maximal clique enumeration is a fundamental graph mining task, but its utility is often limited by computational intractability and highly redundant output. To address these challenges, we introduce \emph{$\rho$-dense aggregators}, a novel…

Although the inference of global community structure in networks has recently become a topic of great interest in the physics community, all such algorithms require that the graph be completely known. Here, we define both a measure of local…

Community search, retrieving the cohesive subgraph which contains the query vertex, has been widely touched over the past decades. The existing studies on community search mainly focus on static networks. However, real-world networks…

The problem of subgraph counting asks for the number of occurrences of a pattern graph $H$ as a subgraph of a host graph $G$ and is known to be computationally challenging: it is $\#W[1]$-hard even when $H$ is restricted to simple…

We study the space complexity of four variants of the standard subgraph finding problem in the streaming model. Specifically, given an $n$-vertex input graph and a fixed-size pattern graph, we consider two settings: undirected simple…

We describe a data structure that maintains the number of triangles in a dynamic undirected graph, subject to insertions and deletions of edges and of degree-zero vertices. More generally it can be used to maintain the number of copies of…

Given query access to an undirected graph $G$, we consider the problem of computing a $(1\pm\epsilon)$-approximation of the number of $k$-cliques in $G$. The standard query model for general graphs allows for degree queries, neighbor…

Finding large cliques or cliques missing a few edges is a fundamental algorithmic task in the study of real-world graphs, with applications in community detection, pattern recognition, and clustering. A number of effective…

The NP-hard 2-Club problem is, given an undirected graph G=(V,E) and l\in N, to decide whether there is a vertex set S\subseteq V of size at least l such that the induced subgraph G[S] has diameter at most two. We make progress towards a…

A $k$-defective clique is a relaxation of the traditional clique definition, allowing up to $k$ missing edges. This relaxation is crucial in various real-world applications such as link prediction, community detection, and social network…

A clique in an undirected graph G= (V, E) is a subset V' V of vertices, each pair of which is connected by an edge in E. The clique problem is an optimization problem of finding a clique of maximum size in graph. The clique problem is…

We address the problem of computing a Minimal Dominating Set in highly dynamic distributed systems. We assume weak connectivity, i.e., the network may be disconnected at each time instant and topological changes are unpredictable. We make…

We propose an efficient linear-time graph-based divisive cluster analysis approach called Reductive Clustering. The approach tries to reveal the hierarchical structural information through reducing the graph into a more concise one…

We study the complexity of a classic problem in computational topology, the homology problem: given a description of some space $X$ and an integer $k$, decide if $X$ contains a $k$-dimensional hole. The setting and statement of the homology…

We propose a hybrid heuristic algorithm for solving the Heaviest k-Subgraph Problem in online social networks -- a combinatorial graph optimization problem central to many important applications in weighted social networks, including…

Single-linkage clustering is a popular form of hierarchical agglomerative clustering (HAC) where the distance between two clusters is defined as the minimum distance between any pair of points across the two clusters. In single-linkage HAC,…

We consider the minimal k-grouping problem: given a graph G=(V,E) and a constant k, partition G into subgraphs of diameter no greater than k, such that the union of any two subgraphs has diameter greater than k. We give a silent…

This paper presents efficient distributed algorithms for a number of fundamental problems in the area of graph sparsification: We provide the first deterministic distributed algorithm that computes an ultra-sparse spanner in…