
(FPT)Approximation Algorithms for the Virtual Network Embedding Problem
Many resource allocation problems in the cloud can be described as a bas...
read it

NodeConnectivity Terminal Backup, SeparatelyCapacitated Multiflow, and Discrete Convexity
The terminal backup problems (Anshelevich and Karagiozova (2011)) form a...
read it

Defending with Shared Resources on a Network
In this paper we consider a defending problem on a network. In the model...
read it

Simple Combinatorial Algorithms for the Minimum Dominating Set Problem in Bounded Arboricity Graphs
We revisit the minimum dominating set problem on graphs with arboricity ...
read it

Cycles to the Rescue! Novel Constraints to Compute Maximum Planar Subgraphs Fast
The NPhard Maximum Planar Subgraph problem asks for a planar subgraph H...
read it

A Hitting Set Relaxation for kServer and an Extension to TimeWindows
We study the kserver problem with timewindows. In this problem, each r...
read it

On the minimum quartet tree cost problem
Given a set of n data objects and their pairwise dissimilarities, the go...
read it
Virtual Network Embedding via Decomposable LP Formulations: Orientations of Small Extraction Width and Beyond
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 fixedparameter 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 halfwheel 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 NPhard. 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 intersubgraph boundary. In particular, the algorithm has zero additional cost when subgraphs are separated by a single node.
READ FULL TEXT
Comments
There are no comments yet.