Related papers: Fractional Graph Coloring for Functional Compressi…
Coloring is one of the most famous problems in graph theory. The coloring problem on undirected graphs has been well studied, whereas there are very few results for coloring problems on directed graphs. An oriented k-coloring of an oriented…
One method to obtain a proper vertex coloring of graphs using a reasonable number of colors is to start from any arbitrary proper coloring and then repeat some local re-coloring techniques to reduce the number of color classes. The Grundy…
Conceptual coding has been an emerging research topic recently, which encodes natural images into disentangled conceptual representations for compression. However, the compression performance of the existing methods is still sub-optimal due…
We design a low complexity distributed compression scheme for computing arbitrary functions of sources with discrete alphabets. We use a helper-based method that extends the definition of the G{\'a}cs-K{\"o}rner-Witsenhausen (GKW) common…
We resolve a number of long-standing open problems in online graph coloring. More specifically, we develop tight lower bounds on the performance of online algorithms for fundamental graph classes. An important contribution is that our…
We study the problem of counting $k$-hypergraphlets, an interesting but surprisingly ignored primitive, with the aim of understanding whether efficient algorithms exist. To this end, we consider color coding, a well-known technique for…
Given a finite directed graph, a coloring of its edges turns the graph into a finite-state automaton. A k-synchronizing word of a deterministic automaton is a word in the alphabet of colors at its edges that maps the state set of the…
Many variations of the classical graph coloring model have been intensively studied due to their multiple applications; scheduling problems and aircraft assignments, for instance, motivate the robust coloring problem. This model gets to…
There are many concepts of signed graph coloring which are defined by assigning colors to the vertices of the graphs. These concepts usually differ in the number of self-inverse colors used. We introduce a unifying concept for this kind of…
This study addresses the challenge of, without training or fine-tuning, controlling the global color aspect of images generated with a diffusion model. We rewrite the guidance equations to ensure that the outputs are closer to a known color…
We present a one-shot method for compressing large labeled graphs called Random Edge Coding. When paired with a parameter-free model based on P\'olya's Urn, the worst-case computational and memory complexities scale quasi-linearly and…
This paper explores the application of a new algebraic method of color exchanges to the edge coloring of simple graphs. Vizing's theorem states that the edge coloring of a simple graph $G$ requires either $\Delta$ or $\Delta+1$ colors,…
Current quantum computing devices have different strengths and weaknesses depending on their architectures. This means that flexible approaches to circuit design are necessary. We address this task by introducing a novel space-efficient…
Recent breakthroughs in graph streaming have led to the design of single-pass semi-streaming algorithms for various graph coloring problems such as $(\Delta+1)$-coloring, degeneracy-coloring, coloring triangle-free graphs, and others. These…
This paper introduces the idea of the color Clifford Hardy signal, which can be used to process color images. As a complex analytic function's high-dimensional analogue, the color Clifford Hardy signal inherits many desirable qualities of…
Visual data compression is shifting from human-centered reconstruction to machine-oriented representation coding. In this setting, an image is often mapped to a compact semantic embedding, which is then compressed and transmitted for…
Graph coloring is a problem with varied applications in industry and science such as scheduling, resource allocation, and circuit design. The purpose of this paper is to establish if a new gradient based iterative solver framework known as…
We study combinatorial indicators related to the characteristic phase transitions associated with coloring a graph optimally and finding a maximum independent set. In particular, we investigate the role of the acyclic orientations of the…
In order to make more complex number-based strings from topological coding for defending against the intelligent attacks equipped with quantum computing and providing effective protection technology for the age of quantum computing, we will…
Conformal prediction provides rigorous, distribution-free uncertainty guarantees, but often yields prohibitively large prediction sets in structured domains such as routing, planning, or sequential recommendation. We introduce "graph-based…