Related papers: On the Probe Complexity of Local Computation Algor…
The Massive Parallel Computation (MPC) model is a theoretical framework for popular parallel and distributed platforms such as MapReduce, Hadoop, or Spark. We consider the task of computing a large matching or small vertex cover in this…
We develop an algorithmic framework for graph colouring that reduces the problem to verifying a local probabilistic property of the independent sets. With this we give, for any fixed $k\ge 3$ and $\varepsilon>0$, a randomised…
Non-Local Attention (NLA) is a powerful technique for capturing long-range feature correlations in deep single image super-resolution (SR). However, NLA suffers from high computational complexity and memory consumption, as it requires…
We present a dynamic algorithm for the recognition of proper circular-arc (PCA) graphs, that supports the insertion and removal of vertices (together with its incident edges). The main feature of the algorithm is that it outputs a minimally…
Recently, Graph Neural Network (GNN)-based vulnerability detection systems have achieved remarkable success. However, the lack of explainability poses a critical challenge to deploy black-box models in security-related domains. For this…
The mathematical analysis of robustness and error-tolerance of complex networks has been in the center of research interest. On the other hand, little work has been done when the attack-tolerance of the vertices or edges are not independent…
We introduce the notion of locally identifying coloring of a graph. A proper vertex-coloring c of a graph G is said to be locally identifying, if for any adjacent vertices u and v with distinct closed neighborhood, the sets of colors that…
The rise of graph analytic systems has created a need for ways to measure and compare the capabilities of these systems. Graph analytics present unique scalability difficulties. The machine learning, high performance computing, and visual…
Effective resistance is an important metric that measures the similarity of two vertices in a graph. It has found applications in graph clustering, recommendation systems and network reliability, among others. In spite of the importance of…
This paper initiates formal analysis of a simple, distributed algorithm for community detection on networks. We analyze an algorithm that we call \textsc{Max-LPA}, both in terms of its convergence time and in terms of the "quality" of the…
The CONNECTED VERTEX COVER problem asks for a vertex cover in a graph that induces a connected subgraph. The problem is known to be fixed-parameter tractable (FPT), and is unlikely to have a polynomial sized kernel (under complexity…
Correlation Power Analysis (CPA) is a type of power analysis based side channel attack that can be used to derive the secret key of encryption algorithms including DES (Data Encryption Standard) and AES (Advanced Encryption Standard). A…
Community detection is the problem of identifying natural divisions in networks. Efficient parallel algorithms for identifying such divisions are critical in a number of applications. This report presents an optimized implementation of the…
Learning causal relations from observational data is a fundamental problem with wide-ranging applications across many fields. Constraint-based methods infer the underlying causal structure by performing conditional independence tests.…
Given a graph $G$ and a positive integer $k$, the 2-Load coloring problem is to check whether there is a $2$-coloring $f:V(G) \rightarrow \{r,b\}$ of $G$ such that for every $i \in \{r,b\}$, there are at least $k$ edges with both end…
The vertex cover problem is a fundamental and widely studied combinatorial optimization problem. It is known that its standard linear programming relaxation is integral for bipartite graphs and half-integral for general graphs. As a…
A recent line of research concerns the problem of soft happy colouring (SHC), which requires that a partially coloured graph be extended to a complete colouring to maximise local agreements, so that as many vertices as possible end up…
A proof labelling scheme for a graph class $\mathcal{C}$ is an assignment of certificates to the vertices of any graph in the class $\mathcal{C}$, such that upon reading its certificate and the certificates of its neighbors, every vertex…
Vertex similarity is a major problem in network science with a wide range of applications. In this work we provide novel perspectives on finding (dis)similar vertices within a network and across two networks with the same number of vertices…
In graph sparsification, the goal has almost always been of {global} nature: compress a graph into a smaller subgraph ({sparsifier}) that maintains certain features of the original graph. Algorithms can then run on the sparsifier, which in…