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Approximation Scheme for Lowest Outdegree Orientation and Graph Density Measures

Kowalik, L. (2006). Approximation Scheme for Lowest Outdegree Orientation and Graph Density Measures. In Algorithms and Computation: 17th International Symposium, ISAAC 2006 (pp. 557-566). Berlin, Germany: Springer.

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Genre: Conference Paper

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### Creators

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Creators:
Kowalik, Lukasz1, Author
Asano, Tetsuo1, Editor
Affiliations:
1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019

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Abstract: We deal with the problem of finding such an orientation of a given graph that the largest number of edges leaving a vertex (called the outdegree of the orientation) is small. For any $\varepsilon\in(0,1)$ we show an $\tilde{O}(|E(G)|/\varepsilon)$ time algorithm which finds an orientation of an input graph $G$ with outdegree at most $\lceil(1+\varepsilon)d^*\rceil$, where $d^*$ is the maximum density of a subgraph of $G$. It is known that the optimal value of orientation outdegree is $\lceil d^* \rceil$. Our algorithm has applications in constructing labeling schemes, introduced by Kannan et al. and in approximating such graph density measures as arboricity, pseudoarboricity and maximum density. Our results improve over the previous, 2-approximation algorithms by Aichholzer et al. (for orientation / pseudoarboricity), by Arikati et al. (for arboricity) and by Charikar (for maximum density).

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Language(s): eng - English
Dates: 2007-04-252006
Publication Status: Published in print
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Rev. Type: -
Identifiers: eDoc: 314645
Degree: -

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Title: Untitled Event
Place of Event: Kolkata, India
Start-/End Date: 2006-12-18

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### Source 1

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Title: Algorithms and Computation : 17th International Symposium, ISAAC 2006
Source Genre: Proceedings
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Publ. Info: Berlin, Germany : Springer
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 557 - 566 Identifier: ISBN: 978-3-540-49694-6

### Source 2

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Title: Lecture Notes in Computer Science
Source Genre: Series
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Pages: - Volume / Issue: 4288 Sequence Number: - Start / End Page: - Identifier: -