Related papers: Parameterized Aspects of Triangle Enumeration
A planar orthogonal drawing {\Gamma} of a connected planar graph G is a geometric representation of G such that the vertices are drawn as distinct points of the plane, the edges are drawn as chains of horizontal and vertical segments, and…
The performance of graph algorithms is often measured in terms of the number of traversed edges per second (TEPS). However, this performance metric is inadequate for a graph operation such as exact triangle counting. In triangle counting,…
During recent years the field of fine-grained complexity has bloomed to produce a plethora of results, with both applied and theoretical impact on the computer science community. The cornerstone of the framework is the notion of…
Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…
Partitioning a graph into balanced components is important for several applications. For multi-objective problems, it is useful not only to find one solution but also to enumerate all the solutions with good values of objectives. However,…
Massive sizes of real-world graphs, such as social networks and web graph, impose serious challenges to process and perform analytics on them. These issues can be resolved by working on a small summary of the graph instead . A summary is a…
Many combinatorial optimization problems can be phrased in the language of constraint satisfaction problems. We introduce a graph neural network architecture for solving such optimization problems. The architecture is generic; it works for…
A tree decomposition of a graph facilitates computations by grouping vertices into bags that are interconnected in an acyclic structure, hence their importance in a plethora of problems such as query evaluation over databases and inference…
Parameterised subgraph counting problems are the most thoroughly studied topic in the theory of parameterised counting, and there has been significant recent progress in this area. Many of the existing tractability results for parameterised…
Over the past decade, we witness an increasing amount of interest in the design of exact exponential-time and parameterized algorithms for problems in Graph Drawing. Unfortunately, we still lack knowledge of general methods to develop such…
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…
This paper studies the kernelization complexity of graph coloring problems with respect to certain structural parameterizations of the input instances. We are interested in how well polynomial-time data reduction can provably shrink…
The theme of this paper is how to find all instances of a given "sample" graph in a larger "data graph," using a single round of map-reduce. For the simplest sample graph, the triangle, we improve upon the best known such algorithm. We then…
In parameterized algorithmics, the process of kernelization is defined as a polynomial time algorithm that transforms the instance of a given problem to an equivalent instance of a size that is limited by a function of the parameter. As,…
In this short note, we give a novel algorithm for $O(1)$ round triangle counting in bounded arboricity graphs. Counting triangles in $O(1)$ rounds (exactly) is listed as one of the interesting remaining open problems in the recent survey of…
The key to reconciling the polynomial-time intractability of many machine learning tasks in the worst case with the surprising solvability of these tasks by heuristic algorithms in practice seems to be exploiting restrictions on real-world…
Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject…
A fundamental challenge in graph mining is the ever-increasing size of datasets. Graph summarization aims to find a compact representation resulting in faster algorithms and reduced storage needs. The flip side of graph summarization is the…
A significant portion of the data today, e.g, social networks, web connections, etc., can be modeled by graphs. A proper analysis of graphs with Machine Learning (ML) algorithms has the potential to yield far-reaching insights into many…
We study kernelization of classic hard graph problems when the input graphs fulfill triadic closure properties. More precisely, we consider the recently introduced parameters closure number $c$ and the weak closure number $\gamma$ [Fox et…