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Priority algorithms with advice for disjoint path allocation problems

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posted on 2024-11-22, 11:34 authored by Hans-Joachim Böckenhauer, Fabian FreiFabian Frei, Silvan Horvath
We analyze the Disjoint Path Allocation problem (DPA) in the priority framework. Motivated by the problem of traffic regulation in communication networks, DPA consists of allocating edge-disjoint paths in a graph. Like an online algorithm, a priority algorithm receives its input sequentially and must output irrevocable decisions for individual input items before having seen the entire input. However, in contrast to the online setting, a priority algorithm may choose an order on the set of all possible input items and the actual input is then presented according to this order. A priority algorithm is thus a natural model for the intuitively well-understood concept of a greedy algorithm. Mainly motivated by their application for proving lower bounds, we also consider priority algorithms with advice, thus measuring the necessary amount of information about the yet unknown parts of the input. Besides considering the classical variant of the DPA problem on paths and the related problem of Length-Weighted DPA, we mainly focus on DPA on trees. We show asymptotically matching upper and lower bounds on the advice necessary for optimality in LWDPA and generalize the known optimality result for DPA on paths to trees with maximal degree at most 3. On trees with higher maximal degree, we prove matching upper and lower bounds on the approximation ratio in the advice-free priority setting as well as upper and lower bounds on the advice necessary to achieve optimality.

History

Primary Research Area

  • Algorithmic Foundations and Cryptography

Journal

Theoretical Computer Science

Volume

1021

Page Range

114942-114942

Publisher

Elsevier

Open Access Type

  • Hybrid

Sub Type

  • Article

BibTeX

@article{Böckenhauer:Frei:Horvath:2024, title = "Priority algorithms with advice for disjoint path allocation problems", author = "Böckenhauer, Hans-Joachim" AND "Frei, Fabian" AND "Horvath, Silvan", year = 2024, month = 10, journal = "Theoretical Computer Science", pages = "114942--114942", publisher = "Elsevier", issn = "0304-3975", doi = "10.1016/j.tcs.2024.114942" }