Randomized online graph coloring

Vishwanathan, Sundar

doi:10.1016/0196-6774(92)90061-g

Cited by 53 publications

(28 citation statements)

References 2 publications

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“…Also, it would be interesting to investigate whether randomization helps in improving the known upper bounds and even beating the lower bounds for deterministic algorithms. To our knowledge, randomized online coloring algorithms have not been studied except for very general classes of graphs (e.g., in [16]) where the results are much weaker than those for disk graphs.…”

Section: Open Problemsmentioning

confidence: 99%

“…For checking whether a new node presented has 16 or more non-overlapping disks of some layer in its neighborhood may require time Ω(n 16 ). This could be decreased to Ω(n 8 ) by changing the constraint so that a disk cannot be classified into a layer if it overlaps with at least 8 mutually non-overlapping disks belonging to this layer.…”

Section: The Upper Boundmentioning

confidence: 99%

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A Tight Bound for Online Coloring of Disk Graphs

Caragiannis

Fishkin

Kaklamanis

et al. 2005

Structural Information and Communication Complexity

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Abstract. We present an improved upper bound on the competitiveness of the online coloring algorithm First-Fit in disk graphs which are graphs representing overlaps of disks on the plane. We also show that this bound is best possible for deterministic online coloring algorithms that do not use the disk representation of the input graph. We also present a related new lower bound for unit disk graphs.

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Section: Open Problemsmentioning

confidence: 99%

Section: The Upper Boundmentioning

confidence: 99%

A Tight Bound for Online Coloring of Disk Graphs

Caragiannis

Fishkin

Kaklamanis

et al. 2005

Structural Information and Communication Complexity

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“…3 The links are then colored via distributed randomized coloring [27], where two links i and j are allocated a different color if i ∈ C j or j ∈ C i . This results in each link having a color or a preferred sub-band, m …”

Section: Resource Selectionmentioning

confidence: 99%

Cell Association and Interference Coordination in Heterogeneous LTE-A Cellular Networks

Madan

Borran

Sampath

et al. 2010

IEEE J. Select. Areas Commun.

419

258

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Abstract-Embedding pico/femto base-stations and relay nodes in a macro-cellular network is a promising method for achieving substantial gains in coverage and capacity compared to macroonly networks. These new types of base-stations can operate on the same wireless channel as the macro-cellular network, providing higher spatial reuse via cell splitting. However, these base-stations are deployed in an unplanned manner, can have very different transmit powers, and may not have traffic aggregation among many users. This could potentially result in much higher interference magnitude and variability. Hence, such deployments require the use of innovative cell association and inter-cell interference coordination techniques in order to realize the promised capacity and coverage gains. In this paper, we describe new paradigms for design and operation of such heterogeneous cellular networks. Specifically, we focus on cell splitting, range expansion, semi-static resource negotiation on third-party backhaul connections, and fast dynamic interference management for QoS via over-the-air signaling. Notably, our methodologies and algorithms are simple, lightweight, and incur extremely low overhead. Numerical studies show that they provide large gains over currently used methods for cellular networks.

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“…Vishwanathan [Vis90] presents an algorithm for such a model that uses a number of colors within a logarithmic factor of the Wigderson bound.…”

Section: Past Workmentioning

confidence: 99%

New approximation algorithms for graph coloring

Blum

1994

J. ACM

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The problem of coloring a graph with the minimum number of colors is well known to be NP-hard, even restricted to k-colorable graphs for constant k ≥ 3. This paper explores the approximation problem of coloring k-colorable graphs with as few additional colors as possible in polynomial time, with special focus on the case of k = 3.The previous best upper bound on the number of colors needed for coloring 3-colorable nvertex graphs in polynomial time was O( √ n/ √ log n) colors by Berger and Rompel, improving a bound of O( √ n) colors by Wigderson. This paper presents an algorithm to color any 3-colorable graph with O(n 3/8 polylog(n)) colors, thus breaking an "O(n 1/2−o(1) ) barrier". The algorithm given here is based on examining second-order neighborhoods of vertices, rather than just immediate neighborhoods of vertices as in previous approaches. We extend our results to improve the worst-case bounds for coloring k-colorable graphs for constant k > 3 as well.

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Randomized online graph coloring

Cited by 53 publications

References 2 publications

A Tight Bound for Online Coloring of Disk Graphs

A Tight Bound for Online Coloring of Disk Graphs

Cell Association and Interference Coordination in Heterogeneous LTE-A Cellular Networks

New approximation algorithms for graph coloring

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