From cd465118bb782d7127cfe14cd769b78b8a3a89ae 2017-03-13 13:10:40
From: Tom Bannink <tom.bannink@cwi.nl>
Date: 2017-03-13 13:10:40
Subject: [PATCH] Update TODO list in Mathematica notebook

---

diff --git a/showgraphs.m b/showgraphs.m
index f4e1275e013b13cfb135af99cdaf0bfa59a9e57f..727c8ecdb75c486f50a8c841da4e78a4d549d792 100644
--- a/showgraphs.m
+++ b/showgraphs.m
@@ -8,20 +8,18 @@ Needs["ErrorBarPlots`"]
 
 
 (* ::Text:: *)
+(*- Experimental mixing time as function of n. At (n,tau)=(1000,2.5) it seems to be between 10.000 and 20.000 steps.*)
+(**)
 (*- Use different starting point for switch chain that is closer to uniform:*)
 (*   Do configuration model, starting with the vertex with highest degree and keeping track of a "forbidden list" meaning dont pair something that is not allowed*)
 (*   (a) How close is this to uniform ? At least w.r.t. the measure of #triangles*)
 (*   (b) How often does this procedure work/fail. Might still be faster to do switchings from Erdos-Gallai.*)
 (**)
-(*- Improve runtime*)
-(*   (a) Don't remove/add edges from the std::vector. Simply replace them*)
-(*   (b) Better direct triangle counting? (I doubt it)*)
-(*   (b') Better triangle counting by only keeping track of CHANGES in #triangles*)
-(*   (c) Do not choose the three permutations with 1/3 probability: choose the "staying" one with zero probability. Should still be a valid switch chain?*)
-(**)
-(*- Experimental mixing time as function of n. At (n,tau)=(1000,2.5) it seems to be between 10.000 and 20.000 steps.*)
-(**)
 (*- Count #moves that result in +-k triangles (one move could create many triangles at once!)*)
+(**)
+(*- Improve runtime*)
+(*   (a) Better direct triangle counting? (I doubt it)*)
+(*   (b) Better triangle counting by only keeping track of CHANGES in #triangles*)
 
 
 (* ::Subsection:: *)
@@ -34,6 +32,10 @@ Needs["ErrorBarPlots`"]
 (*- Compute  Sum over i<j<k  of  (1-Exp[- d_i d_j / (2E)]) * (1 - Exp[-d_j d_k / (2E)]) * (1 - Exp[-d_k d_i / (2E)]) .*)
 (*  Computing the f(i,j) = (1-Exp[..]) terms is fine, but then computing Sum[ f(i,j) f(j,k) f(i,k) ) ] over n^3 entries is very slow.*)
 (*  *)
+(*  - Improve runtime*)
+(*   (a) Don't remove/add edges from the std::vector. Simply replace them. Done, is way faster for large n.*)
+(*   (b) Do not choose the three permutations with 1/3 probability: choose the "staying" one with zero probability. Should still be a valid switch chain?*)
+(*  *)
 (*  *)