Added fine-grained complexity related work

main.bib

@@ -559,4 +559,35 @@ Maximilian Schleich},
  title = {Factorized Databases},
  volume = {45},
  year = {2016}
-}
+}
+
+@article{virgi-survey,
+  author    = {Virginia Vassilevska Williams},
+  title     = {Some Open Problems in Fine-Grained Complexity},
+  journal   = {{SIGACT} News},
+  volume    = {49},
+  number    = {4},
+  pages     = {29--35},
+  year      = {2018},
+  url       = {https://doi.org/10.1145/3300150.3300158},
+  doi       = {10.1145/3300150.3300158},
+  timestamp = {Tue, 18 Dec 2018 15:19:27 +0100},
+  biburl    = {https://dblp.org/rec/journals/sigact/Williams18.bib},
+  bibsource = {dblp computer science bibliography, https://dblp.org}
+}
+
+@book{param-comp,
+  author    = {J{\"{o}}rg Flum and
+               Martin Grohe},
+  title     = {Parameterized Complexity Theory},
+  series    = {Texts in Theoretical Computer Science. An {EATCS} Series},
+  publisher = {Springer},
+  year      = {2006},
+  url       = {https://doi.org/10.1007/3-540-29953-X},
+  doi       = {10.1007/3-540-29953-X},
+  isbn      = {978-3-540-29952-3},
+  timestamp = {Tue, 16 May 2017 14:24:38 +0200},
+  biburl    = {https://dblp.org/rec/series/txtcs/FlumG06.bib},
+  bibsource = {dblp computer science bibliography, https://dblp.org}
+}
+

related-work-extra.tex

@@ -7,5 +7,4 @@ There is a large body of work on compact using representations of Boolean formul
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section{Parameterized Complexity}\label{sec:param-compl}
 
-In~\Cref{sec:hard}, we utilized common conjectures from fine-grained complexity theory.
-\BG{ATRI: Parameterized complexity discussion}
+In~\Cref{sec:hard}, we utilized common conjectures from fine-grained complexity theory. The notion of $\sharpwonehard$ is a standard notion in {\em parameterized complexity}, which by now is a standard complexity tool in providing data complexity bounds on query processing results~\cite{param-comp}. E.g. the fact that $k$-matching is $\sharpwonehard$ implies that we cannot have an $n^{\Omega(1)}$ runtime. However, these results do not carefully track the exponent in the hardness result. E.g. $\sharpwonehard$ for the general $k$-matching problem does not imply anything specific for the $3$-matching problem. Similar questions has led to intense research into the new sub-field of {\em fine-grained complexity} (see~\cite{virgi-survey}), where we care about the exponent in our hardness assumptions as well-- e.g.~\Cref{conj:graph} is based on the popular {\em Triangle detection hypothesis} in this area (cf.~\cite{triang-hard}).