Note subexponential MIS complexity on geometric graphs in paper

Cite Alber & Fiala (2004) for O*(c^sqrt(n)) algorithms on unit disk,
King's subgraph, and triangular subgraph variants.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

Author: GiggleLiu

docs/paper/reductions.typ

@@ -335,7 +335,7 @@ In all graph problems below, $G = (V, E)$ denotes an undirected graph with $|V|
 #problem-def("MaximumIndependentSet")[
   Given $G = (V, E)$ with vertex weights $w: V -> RR$, find $S subset.eq V$ maximizing $sum_(v in S) w(v)$ such that no two vertices in $S$ are adjacent: $forall u, v in S: (u, v) in.not E$.
 ][
-One of Karp's 21 NP-complete problems @karp1972, MIS appears in wireless network scheduling, register allocation, and coding theory @shannon1956. Solvable in polynomial time on bipartite graphs (König's theorem), interval graphs, chordal graphs, and cographs. The best known algorithm runs in $O^*(1.1996^n)$ time via measure-and-conquer branching @xiao2017.
+One of Karp's 21 NP-complete problems @karp1972, MIS appears in wireless network scheduling, register allocation, and coding theory @shannon1956. Solvable in polynomial time on bipartite graphs (König's theorem), interval graphs, chordal graphs, and cographs. The best known algorithm runs in $O^*(1.1996^n)$ time via measure-and-conquer branching @xiao2017. On geometric graphs (King's subgraph, triangular subgraph, unit disk graphs), MIS admits subexponential $O^*(c^sqrt(n))$ algorithms for some constant $c$, via geometric separation @alber2004.
 
 *Example.* Consider the Petersen graph $G$ with $n = 10$ vertices, $|E| = 15$ edges, and unit weights $w(v) = 1$ for all $v in V$. The graph is 3-regular (every vertex has degree 3). A maximum independent set is $S = {v_1, v_3, v_5, v_9}$ with $w(S) = sum_(v in S) w(v) = 4 = alpha(G)$. No two vertices in $S$ share an edge, and no vertex can be added without violating independence.
 

docs/paper/references.bib

@@ -355,3 +355,14 @@ @article{shannon1956
   doi     = {10.1109/TIT.1956.1056798}
 }
 
+@article{alber2004,
+  author  = {Jochen Alber and Ji\v{r}\'{\i} Fiala},
+  title   = {Geometric separation and exact solutions for the parameterized independent set problem on disk graphs},
+  journal = {Journal of Algorithms},
+  volume  = {52},
+  number  = {2},
+  pages   = {134--151},
+  year    = {2004},
+  doi     = {10.1016/j.jalgor.2003.10.001}
+}
+