相关论文: A new lower bound for the on-line coloring of inte…
We study the online graph coloring problem restricted to the intersection graphs of intervals with lengths in $[1,\sigma]$. For $\sigma=1$ it is the class of unit interval graphs, and for $\sigma=\infty$ the class of all interval graphs.…
A lower bound is obtained for the greatest possible number of colors in an interval colourings of some regular graphs.
We propose two strategies for Presenter in the on-line interval graph coloring games. Specifically, we consider a setting in which each interval is associated with a $d$-dimensional vector of weights and the coloring needs to satisfy the…
We study the online coloring of $\sigma$-interval graphs, which are interval graphs with interval lengths in $[1,\sigma]$ and 2-count interval graphs, which are interval graphs that require at most two distinct interval lengths. For…
In this paper, we study the performance of the FirstFit algorithm for the online unit-length intervals coloring problem where the intervals can be either open or closed, which serves a further investigation towards the actual performance of…
We slightly improve the known lower bound on the asymptotic competitive ratio for online bin packing of rectangles. We present a complete proof for the new lower bound, whose value is above 1.91.
The Minimum Sum Coloring Problem is a variant of the Graph Vertex Coloring Problem, for which each color has a weight. This paper presents a new way to find a lower bound of this problem, based on a relaxation into an integer partition…
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…
An edge coloring of a graph $G$ with colors $1,2,..., t$ is called an interval $t$-coloring if for each $i\in \{1,2,...,t\}$ there is at least one edge of $G$ colored by $i$, the colors of edges incident to any vertex of $G$ are distinct…
We consider the discrepancy problem of coloring $n$ intervals with $k$ colors such that at each point on the line, the maximal difference between the number of intervals of any two colors is minimal. Somewhat surprisingly, a coloring with…
We consider several previously studied online variants of bin packing and prove new and improved lower bounds on the asymptotic competitive ratios for them. For that, we use a method of fully adaptive constructions. In particular, we…
We improve the lower bound on the asymptotic competitive ratio of any online algorithm for bin packing to above 1.54278. We demonstrate for the first time the advantage of branching and the applicability of full adaptivity in the design of…
This paper introduces a variant of the classical edge coloring problem in graphs that can be applied to an offline scheduling problem for crossbar switches. We show that the problem is NP-complete, develop three lower bounds bounds on the…
The lower bound W(K_{2n})>=3n-2 is proved for the greatest possible number of colors in an interval edge coloring of the complete graph K_{2n}.
Kierstead and Trotter (Congressus Numerantium 33, 1981) proved that their algorithm is an optimal online algorithm for the online interval coloring problem. In this paper, for online unit interval coloring, we show that the number of colors…
Rainbow coloring is a special case of edge coloring, where there must be at least one path between every distinct pair of vertices that consists of different color edges. Here, we may use the same color for the adjacent edges of a graph…
We consider the open, non-preemptive online Dial-a-Ride problem on the real line, where transportation requests appear over time and need to be served by a single server. We give a lower bound of 2.0585 on the competitive ratio, which is…
A graph is said to be interval colourable if it admits a proper edge-colouring using palette $\mathbb{N}$ in which the set of colours incident to each vertex is an interval. The interval colouring thickness of a graph $G$ is the minimum $k$…
In this paper we study the problem of coloring a unit interval graph which changes dynamically. In our model the unit intervals are added or removed one at the time, and have to be colored immediately, so that no two overlapping intervals…
In many practical applications the underlying graph must be as equitable colored as possible. A coloring is called equitable if the number of vertices colored with each color differs by at most one, and the least number of colors for which…