Related papers: Proximity Search For Maximal Subgraph Enumeration
For a class $\mathcal{G}$ of graphs, the objective of \textsc{Subgraph Complementation to} $\mathcal{G}$ is to find whether there exists a subset $S$ of vertices of the input graph $G$ such that modifying $G$ by complementing the subgraph…
The branching algorithm is a fundamental technique for designing fast exponential-time algorithms to solve combinatorial optimization problems exactly. It divides the entire solution space into independent search branches using…
Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of…
The Max-Cut problem is a fundamental NP-hard problem, which is attracting attention in the field of quantum computation these days. Regarding the approximation algorithm of the Max-Cut problem, algorithms based on semidefinite programming…
Combinatorial optimization lies at the core of many real-world problems. Especially since the rise of graph neural networks (GNNs), the deep learning community has been developing solvers that derive solutions to NP-hard problems by…
We demonstrate that a graph-based search algorithm-relying on the construction of an approximate neighborhood graph-can directly work with challenging non-metric and/or non-symmetric distances without resorting to metric-space mapping…
Branch-and-bound (BnB) algorithms are widely used to solve combinatorial problems, and the performance crucially depends on its branching heuristic.In this work, we consider a typical problem of maximum common subgraph (MCS), and propose a…
New algorithm for finding longest increasing subsequence is discussed. This algorithm is based on the ideas of idempotent mathematics and uses Max-Plus idempotent semiring. Problem of finding longest increasing sub- sequence is reformulated…
A transitive graph is 2-dimensional if it can be represented as the intersection of two linear orders. Such representations make answering of reachability queries trivial, and allow many problems that are NP-hard on arbitrary graphs to be…
Finding a maximum-weight matching is a classical and well-studied problem in computer science, solvable in cubic time in general graphs. We consider the specialization called assignment problem where the input is a bipartite graph, and…
The densest $k$-subgraph problem is the problem of finding a $k$-vertex subgraph of a graph with the maximum number of edges. In order to solve large instances of the densest $k$-subgraph problem, we introduce two algorithms that are based…
We present a series of almost settled inapproximability results for three fundamental problems. The first in our series is the subexponential-time inapproximability of the maximum independent set problem, a question studied in the area of…
In this work we design graph neural network architectures that capture optimal approximation algorithms for a large class of combinatorial optimization problems, using powerful algorithmic tools from semidefinite programming (SDP).…
Graph embedding has recently gained momentum in the research community, in particular after the introduction of random walk and neural network based approaches. However, most of the embedding approaches focus on representing the local…
In this paper, we consider the problems of enumerating minimal vertex covers and minimal dominating sets with capacity and/or connectivity constraints. We develop polynomial-delay enumeration algorithms for these problems on bounded-degree…
We study the problem of connecting the parts of a multipartite graph using a minimum number of edges under a matching constraint. We introduce interconnection trees, defined as matchings whose projections onto the quotient graph form a…
Given two input graphs, finding the largest subgraph that occurs in both, i.e., finding the maximum common subgraph, is a fundamental operator for evaluating the similarity between two graphs in graph data analysis. Existing works for…
We study the problem of maximizing the number of spanning trees in a connected graph by adding at most $k$ edges from a given candidate edge set. We give both algorithmic and hardness results for this problem: - We give a greedy algorithm…
This paper deals with the problem of finding, for a given graph and a given natural number k, a subgraph of k nodes with a maximum number of edges. This problem is known as the k-cluster problem and it is NP-hard on general graphs as well…
We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…