Virtual Network Embedding via Decomposable LP Formulations: Orientations
of Small Extraction Width and Beyond
release_hhivy7ktsjflbcqze4s764eary
by
Elias Döhne
2018
Abstract
The Virtual Network Embedding Problem (VNEP) considers the efficient
allocation of resources distributed in a substrate network to a set of request
networks. Many existing works discuss either heuristics or exact algorithms,
resulting in a choice between quick runtimes and quality guarantees for the
solutions. Recently, the first fixed-parameter tractable (FPT) approximation
algorithm for the VNEP with arbitrary request and substrate topologies has been
published by Rost and Schmid. This algorithm is based on a LP formulation and
is FPT in the newly introduced graph parameter extraction width (EW). It
therefore combines positive traits of heuristics and exact approaches: The
runtime is polynomial for instances with bounded EW, and the algorithm returns
approximate solutions with high probability.
We propose two extensions of this algorithm to optimize its runtime. Firstly,
we develop a new LP formulation related to tree decompositions. We show that
this LP formulation is always smaller, and that the resulting algorithm is FPT
in the new parameter extraction label width (ELW). We improve on two important
results by Rost and Schmid: For centrally rooted half-wheel topologies, the EW
scales linearly with request size, whereas the ELW is constant. Further, adding
any number of paths parallel to an existing edge increases the EW by at most
the maximum degree of the request. By contrast, the ELW only increases by at
most one. Lastly, we show that finding the minimal ELW is NP-hard.
Secondly, we consider the approach of partitioning the request into subgraphs
which are processed independently, yielding even smaller LP formulations. While
this algorithm may lead to higher ELW within the subgraphs, we show that this
increase is always smaller than the size of the inter-subgraph boundary. In
particular, the algorithm has zero additional cost when subgraphs are separated
by a single node.
In text/plain
format
Archived Files and Locations
application/pdf 2.3 MB
file_iuob5qbzu5eqvgmu73mmlitaai
|
arxiv.org (repository) web.archive.org (webarchive) |
1810.11280v1
access all versions, variants, and formats of this works (eg, pre-prints)