Related papers: Quantum property testing in sparse directed graphs
This paper continues the study of a new variant of graph coloring with a connectivity constraint recently introduced by Hsieh et al. [COCOON 2024]. A path in a vertex-colored graph is called conflict-free if there is a color that appears…
{\em Partial domination problem} is a generalization of the {\em minimum dominating set problem} on graphs. Here, instead of dominating all the nodes, one asks to dominate at least a fraction of the nodes of the given graph by choosing a…
Graph partitioning is one of an important set of well-known compute-intense (NP-hard) graph problems that devolve to discrete constrained optimization. We sampled solutions to the problem via two different quantum-ready methods to…
We study in this paper the structure of solutions in the random hypergraph coloring problem and the phase transitions they undergo when the density of constraints is varied. Hypergraph coloring is a constraint satisfaction problem where…
We study graph coloring problems in the streaming model, where the goal is to process an $n$-vertex graph whose edges arrive in a stream, using a limited space that is smaller than the trivial $O(n^2)$ bound. While prior work has largely…
In property testing, a tester makes queries to (an oracle for) a graph and, on a graph having or being far from having a property P, it decides with high probability whether the graph satisfies P or not. Often, testers are restricted to a…
In this paper, we investigate the $k$-path coloring problem, a variant of vertex coloring arising in the context of integrated circuit manufacturing. In this setting, typical industrial instances exhibit a `tree-like' structure. We exploit…
This paper introduces an efficient quantum computing method for reducing special graphs in the context of the graph coloring problem. The special graphs considered include both symmetric and non-symmetric graphs where the axis passes…
Quantum hypothesis testing is one of the most fundamental problems in quantum information theory, with crucial implications in areas like quantum sensing, where it has been used to prove quantum advantage in a series of binary photonic…
We establish nearly optimal sample complexity bounds for testing the $\rho$-clique property in the dense graph model. Specifically, we show that it is possible to distinguish graphs on $n$ vertices that have a $\rho n$-clique from graphs…
We give an almost complete characterization of the hardness of $c$-coloring $\chi$-chromatic graphs with distributed algorithms, for a wide range of models of distributed computing. In particular, we show that these problems do not admit…
For a positive integer $k$, a $k$-colouring of a graph $G=(V,E)$ is a mapping $c: V\rightarrow\{1,2,...,k\}$ such that $c(u)\neq c(v)$ whenever $uv\in E$. The Colouring problem is to decide, for a given $G$ and $k$, whether a $k$-colouring…
This paper addresses the problem of finding the densest $k$-vertex subgraph in an arbitrary graph. This problem is NP-hard and has important applications in social network analysis, fraud detection, recommendation systems, and…
We consider the Densest-Subgraph problem, where a graph and an integer k is given and we search for a subgraph on exactly k vertices that induces the maximum number of edges. We prove that this problem is NP-hard even when the input graph…
The notions of bounded expansion and nowhere denseness not only offer robust and general definitions of uniform sparseness of graphs, they also describe the tractability boundary for several important algorithmic questions. In this paper we…
We analyse uniformly random proper $k$-colourings of sparse graphs with maximum degree $\Delta$ in the regime $\Delta < k\ln k $. This regime corresponds to the lower side of the shattering threshold for random graph colouring, a…
In this paper, we consider the parameterized quantum query complexity for graph problems. We design parameterized quantum query algorithms for $k$-vertex cover and $k$-matching problems, and present lower bounds on the parameterized quantum…
Graphs are naturally sparse objects that are used to study many problems involving networks, for example, distributed learning and graph signal processing. In some cases, the graph is not given, but must be learned from the problem and…
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…
Sublinear time algorithms represent a new paradigm in computing, where an algorithm must give some sort of an answer after inspecting only a small portion of the input. The most typical situation where sublinear time algorithms are…