Related papers: On the FirstFit Algorithm for Online Unit-Interval…
We study online interval scheduling in the irrevocable setting, where each interval must be immediately accepted or rejected upon arrival. The objective is to maximize the total length of accepted intervals while ensuring that no two…
An edge-coloring of a multigraph G with colors 1,2,...,t is called an interval t-coloring if all colors are used, and the colors of edges incident to any vertex of G are distinct and form an interval of integers. In this paper we prove that…
Image learning and colorization are hot spots in multimedia domain. Inspired by the learning capability of humans, in this paper, we propose an automatic colorization method with a learning framework. This method can be viewed as a hybrid…
Given a large social or information network, how can we partition the vertices into sets (i.e., colors) such that no two vertices linked by an edge are in the same set while minimizing the number of sets used. Despite the obvious practical…
Vizing's theorem states that any $n$-vertex $m$-edge graph of maximum degree $\Delta$ can be {\em edge colored} using at most $\Delta + 1$ different colors [Diskret.~Analiz, '64]. Vizing's original proof is algorithmic and shows that such…
Following a line of work that takes advantage of vast machine-learned data to enhance online algorithms with (possibly erroneous) information about future inputs, we consider predictions in the context of deterministic algorithms for the…
One of the fundamental and most-studied algorithmic problems in distributed computing on networks is graph coloring, both in bounded-degree and in general graphs. Recently, the study of this problem has been extended in two directions.…
In this paper, we consider algorithms for edge-coloring multigraphs $G$ of bounded maximum degree, i.e., $\Delta(G) = O(1)$. Shannon's theorem states that any multigraph of maximum degree $\Delta$ can be properly edge-colored with…
Color sequences, ordered sets of colors for data visualization, that balance aesthetics with accessibility considerations are presented. In order to model aesthetic preference, data were collected with an online survey, and the results were…
The online bin packing problem and its variants are regularly used to model server allocation problems. Modern concerns surrounding sustainability and overcommitment in cloud computing motivate bin packing models that capture costs…
The $H$-Coloring problem is a well-known generalization of the classical NP-complete problem $k$-Coloring where the task is to determine whether an input graph admits a homomorphism to the template graph $H$. This problem has been the…
For complete graphs and n-cubes bounds are found for the possible number of colours in an interval edge colourings.
We prove new bounds on the distributed fractional coloring problem in the LOCAL model. Fractional $c$-colorings can be understood as multicolorings as follows. For some natural numbers $p$ and $q$ such that $p/q\leq c$, each node $v$ is…
An edge-coloring of a graph $G$ with colors $1,\ldots,t$ is called an \emph{interval $t$-coloring} if all colors are used and the colors of edges incident to each vertex of $G$ are distinct and form an interval of integers. In 1990,…
We introduce a novel measure for quantifying the error in input predictions. The error is based on a minimum-cost hyperedge cover in a suitably defined hypergraph and provides a general template which we apply to online graph problems. The…
MeanShift algorithm has been widely used in tracking tasks because of its simplicity and efficiency. However, the traditional MeanShift algorithm needs to label the initial region of the target, which reduces the applicability of the…
Vizing's theorem states that any graph of maximum degree $\Delta$ can be properly edge colored with at most $\Delta+1$ colors. In the online setting, it has been a matter of interest to find an algorithm that can properly edge color any…
The filtering-clustering models, including trend filtering and convex clustering, have become an important source of ideas and modeling tools in machine learning and related fields. The statistical guarantee of optimal solutions in these…
In FOCS'2002, Even et al. introduced and studied the notion of conflict-free colorings of geometrically defined hypergraphs. They motivated it by frequency assignment problems in cellular networks. This notion has been extensively studied…
Fixed-parameter algorithms have been successfully applied to solve numerous difficult problems within acceptable time bounds on large inputs. However, most fixed-parameter algorithms are inherently \emph{sequential} and, thus, make no use…