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Electronic Colloquium on Computational Complexity

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REPORTS > KEYWORD > BOUNDED DEGREE GRAPHS:
Reports tagged with bounded degree graphs:
TR00-021 | 19th April 2000
Uriel Feige, Marek Karpinski, Michael Langberg

Improved Approximation of MAX-CUT on Graphs of Bounded Degree

We analyze the addition of a simple local improvement step to various known
randomized approximation algorithms.
Let $\alpha \simeq 0.87856$ denote the best approximation ratio currently
known for the Max Cut problem on general graphs~\cite{GW95}.
We consider a semidefinite relaxation of the Max Cut problem,
round it using the ... more >>>


TR06-089 | 16th July 2006
Sofya Raskhodnikova, Adam Smith

A Note on Adaptivity in Testing Properties of Bounded Degree Graphs

We show that in the bounded degree model for graph property testing,
adaptivity is essential. An algorithm is *non-adaptive* if it makes all queries to the input before receiving any answers. We call a property *non-trivial* if it does not depend only on the degree distribution of the nodes. We ... more >>>


TR18-101 | 20th May 2018
Akash Kumar, C. Seshadhri, Andrew Stolman

Finding forbidden minors in sublinear time: a $O(n^{1/2+o(1)})$-query one-sided tester for minor closed properties on bounded degree graphs

Let $G$ be an undirected, bounded degree graph with $n$ vertices. Fix a finite graph $H$, and suppose one must remove $\varepsilon n$ edges from $G$ to make it $H$-minor free (for some small constant $\varepsilon > 0$).
We give an $n^{1/2+o(1)}$-time randomized procedure that, with high probability, finds an ... more >>>


TR18-148 | 25th August 2018
Akash Kumar, C. Seshadhri, Andrew Stolman

Finding forbidden minors in sublinear time: a $n^{1/2+o(1)}$-query one-sided tester for minor closed properties on bounded degree graphs

Let $G$ be an undirected, bounded degree graph
with $n$ vertices. Fix a finite graph $H$, and suppose one must remove $\varepsilon n$ edges from $G$ to make it $H$-minor free (for some small constant $\varepsilon > 0$). We give an $n^{1/2+o(1)}$-time randomized procedure that, with high probability, finds an ... more >>>


TR21-122 | 24th August 2021
Sabyasachi Basu, Akash Kumar, C. Seshadhri

The complexity of testing all properties of planar graphs, and the role of isomorphism

Consider property testing on bounded degree graphs and let $\varepsilon > 0$ denote the proximity parameter. A remarkable theorem of Newman-Sohler (SICOMP 2013) asserts that all properties of planar graphs (more generally hyperfinite) are testable with query complexity only depending on $\varepsilon$. Recent advances in testing minor-freeness have proven that ... more >>>


TR22-184 | 28th December 2022
Oded Goldreich, Laliv Tauber

Testing in the bounded-degree graph model with degree bound two

Considering the bounded-degree graph model, we show that if the degree bound is two,
then every graph property can be tested within query complexity that only depends on the proximity parameter.
Specifically, the query complexity is ${\rm poly}(1/\epsilon)$, where $\epsilon$ denotes the proximity parameter.
The key observation is that a ... more >>>




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