Related papers: A colouring protocol for the generalized Russian c…
We study the behavior of the Douglas-Rachford algorithm on the graph vertex-coloring problem. Given a graph and a number of colors, the goal is to find a coloring of the vertices so that all adjacent vertex pairs have different colors. In…
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…
A coloring of edges of a finite directed graph turns the graph into finite-state automaton. The synchronizing word of a deterministic automaton is a word in the alphabet of colors (considered as letters) of its edges that maps the automaton…
In recent years, neural networks have been used to implement symmetric cryptographic functions for secure communications. Extending this domain, the proposed approach explores the application of asymmetric cryptography within a neural…
We study the role of interaction in the Common Randomness Generation (CRG) and Secret Key Generation (SKG) problems. In the CRG problem, two players, Alice and Bob, respectively get samples $X_1,X_2,\dots$ and $Y_1,Y_2,\dots$ with the pairs…
Conditional disclosure of secrets (CDS) is the problem of disclosing as efficiently as possible, one secret from Alice and Bob to Carol if and only if the inputs at Alice and Bob satisfy some function $f$. The information theoretic capacity…
The strategies adopted by individuals to select relevant information to pass on are central to understanding problem solving by groups. Here we use agent-based simulations to revisit a cooperative problem-solving scenario where the task is…
An injective colouring of a graph is a colouring in which every two vertices sharing a common neighbour receive a different colour. Chen, Hahn, Raspaud and Wang conjectured that every planar graph of maximum degree $\Delta \ge 3$ admits an…
The generalised colouring numbers $\mathrm{adm}_r(G)$, $\mathrm{col}_r(G)$, and $\mathrm{wcol}_r(G)$ were introduced by Kierstead and Yang as generalisations of the usual colouring number, also known as the degeneracy of a graph, and have…
The polynomial method from circuit complexity has been applied to several fundamental problems and obtains the state-of-the-art running times. As observed in [Alman and Williams, STOC 2017], almost all applications of the polynomial method…
We consider the problem of polar coding for secure communications over the two-way wiretap channel, where two legitimate users communicate with each other simultaneously while a passive eavesdropper overhears a combination of their…
Distributed vertex coloring is one of the classic problems and probably also the most widely studied problems in the area of distributed graph algorithms. We present a new randomized distributed vertex coloring algorithm for the standard…
The graph coloring problem (GCP) is one of the most studied NP-HARD problems in computer science. Given a graph , the task is to assign a color to all vertices such that no vertices sharing an edge receive the same color and that the number…
DP-coloring (also known as correspondence coloring) is a generalization of list coloring introduced recently by Dvo\v{r}\'ak and Postle (2017). In this paper, we prove that every planar graph $G$ without $4$-cycles adjacent to $k$-cycles is…
We give a near-linear time 4-coloring algorithm for planar graphs, improving on the previous quadratic time algorithm by Robertson et al. from 1996. Such an algorithm cannot be achieved by the known proofs of the Four Color Theorem (4CT).…
We propose a cryptographic scheme that is deterministic: Alice sends single photons to Bob, and each and every photon detected supplies one key bit -- no photon is wasted. This is in marked contrast to other schemes in which a random…
A class domination coloring (also called cd-Coloring or dominated coloring) of a graph is a proper coloring in which every color class is contained in the neighbourhood of some vertex. The minimum number of colors required for any…
The coloring problem (i.e., computing the chromatic number of a graph) can be solved in $O^*(2^n)$ time, as shown by Bj\"orklund, Husfeldt and Koivisto in 2009. For $k=3,4$, better algorithms are known for the $k$-coloring problem.…
Hat problems have recently become a popular topic in combinatorics and discrete mathematics. These have been shown to be strongly related to coding theory, network coding, and auctions. We consider the following version of the hat game,…
Prepare and measure quantum key distribution protocols can be decomposed into two basic steps: delivery of the signals over a quantum channel and distillation of a secret key from the signal and measurement records by classical processing…