Abstract | ||
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Dynamic Complexity was introduced by Immerman and Patnaik \cite{PatnaikImmerman97} (see also \cite{DongST95}). It has seen a resurgence of interest in the recent past, see \cite{DattaHK14,ZeumeS15,MunozVZ16,BouyerJ17,Zeume17,DKMSZ18,DMVZ18,BarceloRZ18,DMSVZ19,SchmidtSVZK20,DKMTVZ20} for some representative examples. Use of linear algebra has been a notable feature of some of these papers. We extend this theme to show that the gap version of spectral expansion in bounded degree graphs can be maintained in the class $\DynACz$ (also known as $\dynfo$, for domain independent queries) under batch changes (insertions and deletions) of $O(\frac{\log{n}}{\log{\log{n}}})$ many edges. The spectral graph theoretic material of this work is based on the paper by Kale-Seshadri \cite{KaleS11}. Our primary technical contribution is to maintain up to logarithmic powers of the transition matrix of a bounded degree undirected graph in $\DynACz$. |
Year | DOI | Venue |
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2021 | 10.1007/978-3-030-79416-3_4 | CSR |
DocType | Citations | PageRank |
Conference | 0 | 0.34 |
References | Authors | |
0 | 3 |
Name | Order | Citations | PageRank |
---|---|---|---|
Samir Datta | 1 | 0 | 1.69 |
Anuj Tawari | 2 | 0 | 0.34 |
Yadu Vasudev | 3 | 0 | 1.01 |