Disjoint path allocation with sublinear advice

Gebauer, Heidi; Komm, Dennis; Královič, Rastislav; Královič, Richard; Smula, Jasmin

doi:10.1007/978-3-319-21398-9_33

Publication type:	Conference paper
Type of review:	Peer review (publication)
Title:	Disjoint path allocation with sublinear advice
Authors:	Gebauer, Heidi Komm, Dennis Královič, Rastislav Královič, Richard Smula, Jasmin
DOI:	10.1007/978-3-319-21398-9_33
Proceedings:	Computing and Combinatorics
Page(s):	417
Pages to:	429
Conference details:	21st International Computing and Combinatorics Conference (COCOON 2015), Beijing, China, 4-6 August 2015
Issue Date:	2015
Series:	Lecture Notes in Computer Science
Series volume:	9198
Publisher / Ed. Institution:	Springer
Publisher / Ed. Institution:	Cham
ISBN:	978-3-319-21397-2 978-3-319-21398-9
ISSN:	0302-9743 1611-3349
Language:	English
Subjects:	Competitive ratio; Input length; Online algorithm; Hypergeometric distribution; Deterministic algorithm
Subject (DDC):	500: Natural sciences
Abstract:	We study the disjoint path allocation problem. In this setting, a path P of length L is given, and a sequence of subpaths of P arrives online, one in every time step. Each such path requests a permanent connection between its two end-vertices. An online algorithm can admit or reject such a request; in the former case, none of the involved edges can be part of any other connection. We investigate how much additional binary information (called “advice”) can help to obtain a good solution. It is known that, with roughly log2log2L advice bits, it can be guaranteed that a log2L-competitive solution is computed. In this paper, we prove the surprising result that, with L1−ε advice bits, it is not possible to obtain a solution with a competitive ratio better than (δlog2L)/2, where 0<δ<ε<1. This shows an interesting threshold behavior of the problem. A fairly good competitive ratio, namely log2L, can be obtained with very few advice bits. However, any increase of the advice does not help any further until an almost linear number of advice bits is supplied. Then again, it is also known that linear advice allows for optimality.
URI:	https://digitalcollection.zhaw.ch/handle/11475/15845
Fulltext version:	Published version
License (according to publishing contract):	Licence according to publishing contract
Departement:	School of Engineering
Organisational Unit:	Institute of Applied Mathematics and Physics (IAMP)
Appears in collections:	Publikationen School of Engineering

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Gebauer, H., Komm, D., Královič, R., Královič, R., & Smula, J. (2015). Disjoint path allocation with sublinear advice [Conference paper]. Computing and Combinatorics, 417–429. https://doi.org/10.1007/978-3-319-21398-9_33

Gebauer, H. et al. (2015) ‘Disjoint path allocation with sublinear advice’, in Computing and Combinatorics. Cham: Springer, pp. 417–429. Available at: https://doi.org/10.1007/978-3-319-21398-9_33.

H. Gebauer, D. Komm, R. Královič, R. Královič, and J. Smula, “Disjoint path allocation with sublinear advice,” in Computing and Combinatorics, 2015, pp. 417–429. doi: 10.1007/978-3-319-21398-9_33.

GEBAUER, Heidi, Dennis KOMM, Rastislav KRÁLOVIČ, Richard KRÁLOVIČ und Jasmin SMULA, 2015. Disjoint path allocation with sublinear advice. In: Computing and Combinatorics. Conference paper. Cham: Springer. 2015. S. 417–429. ISBN 978-3-319-21397-2

Gebauer, Heidi, Dennis Komm, Rastislav Královič, Richard Královič, and Jasmin Smula. 2015. “Disjoint Path Allocation with Sublinear Advice.” Conference paper. In Computing and Combinatorics, 417–29. Cham: Springer. https://doi.org/10.1007/978-3-319-21398-9_33.

Gebauer, Heidi, et al. “Disjoint Path Allocation with Sublinear Advice.” Computing and Combinatorics, Springer, 2015, pp. 417–29, https://doi.org/10.1007/978-3-319-21398-9_33.