• Corpus ID: 233473858

Structural Rounding on a Parameterized Graph Class using Heuristics

  title={Structural Rounding on a Parameterized Graph Class using Heuristics},
  author={Cole Perschon},
Structural rounding is a framework for approximating NP-hard optimization problems on graphs near structured classes [10]. It has previously been empirically shown to outperform standard 2-approximations for VERTEX COVER on near-bipartite graphs [21]. Though promising, it is unclear if these findings are representative of structural rounding in general since the remainder of the framework’s theoretical results have yet to be tested in practice. In this thesis, we consider the problem of… 


Structural Rounding: Approximation Algorithms for Graphs Near an Algorithmically Tractable Class
New editing algorithms are developed that find the approximately-fewest edits required to bring a given graph into one of several important graph classes (in some cases, also approximating the target parameter of the family).
Approximating Vertex Cover using Structural Rounding
This work provides the first practical evaluation of the structural rounding framework for approximation algorithms, and finds that in this setting, structural rounding significantly outperforms standard 2-approximations.
Improved approximation algorithms for minimum-weight vertex separators
The algorithmic theory of vertex separators, and its relation to the embeddings of certain metric spaces is developed, and an O(√log n) pseudo-approximation for finding balanced vertices in general graphs is exhibited.
Robust Algorithms for on Minor-Free Graphs Based on the Sherali-Adams Hierarchy
This work provides a Linear Programming-based Polynomial Time Approximation Scheme (PTAS) for two classical NP-hard problems on graphs when the input graph is guaranteed to be planar, or more
Approximation Algorithms for Connected Dominating Sets
This work considers the more general problem of finding a connected dominating set of a specified subset of vertices and provides a polynomial time algorithm with a (c+1) H(Δ) +c-1 approximation factor, where c is the Steiner approximation ratio for graphs.
Improved Tree Decomposition Based Algorithms for Domination-like Problems
An O(4kn) algorithm for dominating set, where n is the number of nodes of the tree decomposition, is obtained, which improves the previously best known algorithm of Telle and Proskurowski running in time O(9kn).
Parameterized approximation of dominating set problems
It is shown that there is no FPT algorithm for g(k) of the form k+c (where c is a fixed constant, termed an additive FPT approximation), unless FPT=W[2].
Dynamic Programming on Graphs with Bounded Treewidth
For several NP-complete problems, and subclasses of the graphs with bounded treewidth, polynomial algorithms have been obtained.
Approximating Treewidth, Pathwidth, Frontsize, and Shortest Elimination Tree
Various parameters of graphs connected to sparse matrix factorization and other applications can be approximated using an algorithm of Leighton et al. that finds vertex separators of graphs, and it is shown that unless P = NP there are no absolute approximation algorithms for any of the parameters.
Completeness in approximation classes beyond APX
A reduction is presented that allows to establish completeness results for several approximation classes mainly beyond APX, and a new approximability class, called Poly-APX(Δ), dealing with graph-problems approximable with ratios functions of the maximum degree Δ of the input-graph.