Related papers: Fair densest subgraph across multiple graphs
We study the two inference problems of detecting and recovering an isolated community of \emph{general} structure planted in a random graph. The detection problem is formalized as a hypothesis testing problem, where under the null…
The study of domination in graphs has led to a variety of domination problems studied in the literature. Most of these follow the following general framework: Given a graph $G$ and an integer $k$, decide if there is a set $S$ of $k$…
The subset sum problem is one of the simplest and most fundamental NP-hard problems in combinatorial optimization. We consider two extensions of this problem: The subset sum problem with digraph constraint (SSG) and subset sum problem with…
Graph isomorphism, subgraph isomorphism, and maximum common subgraphs are classical well-investigated objects. Their (parameterized) complexity and efficiently tractable cases have been studied. In the present paper, for a given set of…
Simplifying graphs is a very applicable problem in numerous domains, especially in computational geometry. Given a geometric graph and a threshold, the minimum-complexity graph simplification asks for computing an alternative graph of…
Subgraph similarity search, one of the core problems in graph search, concerns whether a target graph approximately contains a query graph. The problem is recently touched by neural methods. However, current neural methods do not consider…
We give an exact $O(nk^2)$ algorithm for finding the densest k subgraph in outerplanar graphs. We extend this to an exact $O(nk^2 8^b)$ algorithm for finding the densest k subgraph in b-outerplanar graphs. Finally, we hypothesize that…
Tolerance graphs model interval relations in such a way that intervals can tolerate a certain amount of overlap without being in conflict. In one of the most natural generalizations of tolerance graphs with direct applications in the…
The maximum common subtree isomorphism problem asks for the largest possible isomorphism between subtrees of two given input trees. This problem is a natural restriction of the maximum common subgraph problem, which is ${\sf NP}$-hard in…
Graph Neural Networks (GNN) exhibit superior performance in graph representation learning, but their inference cost can be high, due to an aggregation operation that can require a memory fetch for a very large number of nodes. This…
An important objective for analyzing real-world graphs is to achieve scalable performance on large, streaming graphs. A challenging and relevant example is the graph partition problem. As a combinatorial problem, graph partition is NP-hard,…
We investigate the asymptotic number of induced subgraphs in power-law uniform random graphs. We show that these induced subgraphs appear typically on vertices with specific degrees, which are found by solving an optimization problem.…
Graph burning is a simple model for the spread of social influence in networks. The objective is to measure how quickly a fire (e.g., a piece of fake news) can be spread in a network. The burning process takes place in discrete rounds. In…
The explainability of deep networks is becoming a central issue in the deep learning community. It is the same for learning on graphs, a data structure present in many real world problems. In this paper, we propose a method that is more…
The MIT/IEEE/Amazon GraphChallenge.org encourages community approaches to developing new solutions for analyzing graphs and sparse data. Sparse AI analytics present unique scalability difficulties. The proposed Sparse Deep Neural Network…
Everywhere-$\delta$-dense graphs are defined as graphs on $n$ vertices in which every vertex has degree at least $\delta n$ for some constant $\delta > 0$. Approximation schemes are vital for handling NP-hard optimization problems, but for…
The computation of distance measures between nodes in graphs is inefficient and does not scale to large graphs. We explore dense vector representations as an effective way to approximate the same information: we introduce a simple yet…
Given a graph G and the desired size k in bits, how can we summarize G within k bits, while minimizing the information loss? Large-scale graphs have become omnipresent, posing considerable computational challenges. Analyzing such large…
We study the problem of finding a copy of a specific induced subgraph on inhomogeneous random graphs with infinite variance power-law degrees. We provide a fast algorithm that finds a copy of any connected graph $H$ on a fixed number of $k$…
The graph isomorphism problem is considered. We assign modified $n$-variable characteristic polynomials for graphs and reduce the graph isomorphism problem to the problem of the polynomials isomorphism. It is required to find out, is there…