相关论文: On the Capacity of Sequences of Coloring Channels

This paper studies the sequence reconstruction problem for a channel inspired by protein identification. We introduce a coloring channel, where a sequence is transmitted through a channel that deletes all symbols not belonging to a fixed…

Set-coloring a graph means giving each vertex a subset of a fixed color set so that no two adjacent subsets have the same cardinality. When the graph is complete one gets a new distribution problem with an interesting generating function.…

Channel capacity describes the size of the nearly ideal channels, which can be obtained from many uses of a given channel, using an optimal error correcting code. In this paper we collect and compare minor and major variations in the…

To increase the information capacity of DNA storage, composite DNA letters were introduced. We propose a novel channel model for composite DNA in which composite sequences are decomposed into ordered standard non-composite sequences. The…

We study a new variant of \emph{connected coloring} of graphs based on the concept of \emph{strong} edge coloring (every color class forms an \emph{induced} matching). In particular, an edge-colored path is \emph{strongly proper} if its…

A model named `Colored Percolation' has been introduced with its infinite number of versions in two dimensions. The sites of a regular lattice are randomly occupied with probability $p$ and are then colored by one of the $n$ distinct colors…

We derive a single-letter upper bound to the mismatched-decoding capacity for discrete memoryless channels. The bound is expressed as the mutual information of a transformation of the channel, such that a maximum-likelihood decoding error…

One of the primary sequencing methods gaining prominence in DNA storage is nanopore sequencing, attributed to various factors. In this work, we consider a simplified model of the sequencer, characterized as a channel. This channel takes a…

Given two colorings of a graph, we consider the following problem: can we recolor the graph from one coloring to the other through a series of elementary changes, such that the graph is properly colored after each step? We introduce the…

The aim of this paper is to generalize the notion of the coloring complex of a graph to hypergraphs. We present three different interpretations of those complexes -- a purely combinatorial one and two geometric ones. It is shown, that most…

The packing coloring problem has diverse applications, including frequency assignment in wireless networks, resource distribution and facility location in smart cities and post-disaster management, as well as in biological diversity.…

Color and structure are the two pillars that construct an image. Usually, the structure is well expressed through a rich spectrum of colors, allowing objects in an image to be recognized by neural networks. However, under extreme…

The {\em acyclic chromatic number} of a graph is the least number of colors needed to properly color its vertices so that none of its cycles has only two colors. The {\em acyclic chromatic index} is the analogous graph parameter for edge…

This paper demonstrates fundamental limits of sensor networks for detection problems where the number of hypotheses is exponentially large. Such problems characterize many important applications including detection and classification of…

A linear coloring of a graph is a proper coloring of the vertices of the graph so that each pair of color classes induce a union of disjoint paths. In this paper, we prove that for every connected graph with maximum degree at most three and…

Arrangements of pseudolines are a widely studied generalization of line arrangements. They are defined as a finite family of infinite curves in the Euclidean plane, any two of which intersect at exactly one point. One can state various…

Color and structure are the two pillars that combine to give an image its meaning. Interested in critical structures for neural network recognition, we isolate the influence of colors by limiting the color space to just a few bits, and find…

The sequence reconstruction problem involves a model where a sequence is transmitted over several identical channels. This model investigates the minimum number of channels required for the unique reconstruction of the transmitted sequence.…

A coloring of a graph is an assignment of colors to its vertices such that adjacent vertices have different colors. Two colorings are equivalent if they induce the same partition of the vertex set into color classes. Let $\mathcal{A}(G)$ be…

The vertex coloring problem has received a lot of attention in the context of synchronous round-based systems where, at each round, a process can send a message to all its neighbors, and receive a message from each of them. Hence, this…