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We study a variant of online bin packing, called colorful bin packing. In this problem, items that are presented one by one are to be packed into bins of size 1. Each item i has a size s_i \in [0,1] and a color c_i \in C, where C is a set of colors (that is not necessarily known in advance).
Dosa, Gyorgy, Epstein, Leah
openaire +2 more sources
Subdivision into i-packings and S-packing chromatic number of some lattices [PDF]
An $i$-packing in a graph $G$ is a set of vertices at pairwise distance greater than $i$. For a nondecreasing sequence of integers $S=(s\_{1},s\_{2},\ldots)$, the $S$-packing chromatic number of a graph $G$ is the least integer $k$ such that there exists
Gastineau, Nicolas +2 more
core +5 more sources
We study the Colored Bin Packing Problem: we are given a set of items where each item has a weight and color. We must pack the items in bins of uniform capacity such that no two items of the same color may be adjacent within in a bin. The goal is to perform this packing using the fewest number of bins.
Alsarhan, Hamza +4 more
openaire +2 more sources
Modeling the packing coloring problem of graphs
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Z. Shao, A. Vesel
semanticscholar +3 more sources
A Landscape Analysis of Constraint Satisfaction Problems
We discuss an analysis of Constraint Satisfaction problems, such as Sphere Packing, K-SAT and Graph Coloring, in terms of an effective energy landscape.
A. J. Liu +11 more
core +1 more source
A list version of graph packing [PDF]
We consider the following generalization of graph packing. Let $G_{1} = (V_{1}, E_{1})$ and $G_{2} = (V_{2}, E_{2})$ be graphs of order $n$ and $G_{3} = (V_{1} \cup V_{2}, E_{3})$ a bipartite graph.
Győri, Ervin +3 more
core +2 more sources
Deterministic Distributed Edge-Coloring via Hypergraph Maximal Matching
We present a deterministic distributed algorithm that computes a $(2\Delta-1)$-edge-coloring, or even list-edge-coloring, in any $n$-node graph with maximum degree $\Delta$, in $O(\log^7 \Delta \log n)$ rounds.
Fischer, Manuela +2 more
core +1 more source
Two-colorings with many monochromatic cliques in both colors [PDF]
Color the edges of the n-vertex complete graph in red and blue, and suppose that red k-cliques are fewer than blue k-cliques. We show that the number of red k-cliques is always less than cknk, where ck∈(0, 1) is the unique root of the equation zk=(1-z)k ...
Frankl, Péter +3 more
core +1 more source
The role of fibroblast growth factors in cell and cancer metabolism
Fibroblast growth factor (FGF) signaling regulates crucial signaling cascades that promote cell proliferation, survival, and metabolism. Therefore, FGFs and their receptors are often dysregulated in human diseases, including cancer, to sustain proliferation and rewire metabolism.
Jessica Price, Chiara Francavilla
wiley +1 more source
Decomposition of multiple packings with subquadratic union complexity [PDF]
Suppose $k$ is a positive integer and $\mathcal{X}$ is a $k$-fold packing of the plane by infinitely many arc-connected compact sets, which means that every point of the plane belongs to at most $k$ sets.
Pach, János, Walczak, Bartosz
core +2 more sources

