Related papers: Subgraph Counting: Color Coding Beyond Trees
This paper initializes the study of {\em range subgraph counting} and {\em range subgraph listing}, both of which are motivated by the significant demands in practice to perform graph analytics on subgraphs pertinent to only selected, as…
Graph coloring is a computationally difficult problem, and currently the best known classical algorithm for $k$-coloring of graphs on $n$ vertices has runtimes $\Omega(2^n)$ for $k\ge 5$. The list coloring problem asks the following more…
Counting problems, determining the number of possible states of a large system under certain constraints, play an important role in many areas of science. They naturally arise for complex disordered systems in physics and chemistry, in…
The interference imposes a significant negative impact on the performance of wireless networks. With the continuous deployment of larger and more sophisticated wireless networks, reducing interference in such networks is quickly being…
Graph-based computations are crucial in a wide range of applications, where graphs can scale to trillions of edges. To enable efficient training on such large graphs, mini-batch subgraph sampling is commonly used, which allows training…
The problem of finding the densest subgraph in a given graph has several applications in graph mining, particularly in areas like social network analysis, protein and gene analyses etc. Depending on the application, finding dense subgraphs…
Subgraph matching is the problem of determining the presence and location(s) of a given query graph in a large target graph. Despite being an NP-complete problem, the subgraph matching problem is crucial in domains ranging from network…
Motivated by the increasing need to understand the distributed algorithmic foundations of large-scale graph computations, we study some fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$…
The coming quantum computation is forcing us to reexamine the cryptosystems people use. We are applying graph colorings of topological coding to modern information security and future cryptography against supercomputer and quantum computer…
Counting the solution number of combinational optimization problems is an important topic in the study of computational complexity, especially on the #P-complete complexity class. In this paper, we first investigate some organizations of…
Counting the frequency of small subgraphs is a fundamental technique in network analysis across various domains, most notably in bioinformatics and social networks. The special case of triangle counting has received much attention. Getting…
Hypergraphs, describing networks where interactions take place among any number of units, are a natural tool to model many real-world social and biological systems. In this work we propose a principled framework to model the organization of…
Scatterplot selection is an effective approach to represent essential portions of multidimensional data in a limited display space. Various metrics for evaluation of scatterplots such as scagnostics have been presented and applied to…
Colouring sparse graphs under various restrictions is a theoretical problem of significant practical relevance. Here we consider the problem of maximizing the number of different colours available at the nodes and their neighbourhoods,…
Finding a maximum clique in a given graph is one of the fundamental NP-hard problems. We compare two multi-core thread-parallel adaptations of a state-of-the-art branch and bound algorithm for the maximum clique problem, and provide a novel…
Processing large complex networks recently attracted considerable interest. Complex graphs are useful in a wide range of applications from technological networks to biological systems like the human brain. Sometimes these networks are…
We consider a variant of the densest subgraph problem in networks with single or multiple edge attributes. For example, in a social network, the edge attributes may describe the type of relationship between users, such as friends, family,…
Chordal graphs form one of the most studied graph classes. Several graph problems that are NP-hard in general become solvable in polynomial time on chordal graphs, whereas many others remain NP-hard. For a large group of problems among the…
Bounded expansion and nowhere-dense classes of graphs capture the theoretical tractability for several important algorithmic problems. These classes of graphs can be characterized by the so-called weak coloring numbers of graphs, which…
Graph partitioning is a key fundamental problem in the area of big graph computation. Previous works do not consider the practical requirements when optimizing the big data analysis in real applications. In this paper, motivated by…