1,130 reputation
812
bio website andrewdouglasking.com
location Vancouver
age 33
visits member for 4 years, 1 months
seen Apr 10 at 21:04
I am interested in graph theory and combinatorial optimization.

Apr
13
asked A maximum discrepancy hypergraph 2-colouring problem
Apr
9
comment Area ratio of a minimum bounding rectangle of a convex polygon
Right, in other words that the rectangle actually contains the polygon.
Apr
8
answered Area ratio of a minimum bounding rectangle of a convex polygon
Mar
12
comment Gluing two graphs
I think you need to be more specific about your requirements. When you say there are no multiple edges, do you mean that you ignore multiple edges, or that if you identify $u$ with $a$ and $v$ with $b$, then at most one of $uv$, $ab$ is an edge? I assume you are just ignoring multiple edges. If the two sets are cliques or stable sets, then the operation is clique sum or stable set sum. Otherwise you need to be more specific about what vertex mappings are allowed (i.e. if you are identifying $V_1$ and $V_2$, which bijection you use.)
Mar
12
awarded  Yearling
Feb
28
comment Meeting management
I agree that random constructions are a fool's venture; one must pack these partitions into $K_{60}$ with density almost 1/2. Thanks for the insight Kevin. I'm surprised one can go for 11 days under slightly different circumstances.
Feb
27
comment Meeting management
PS Jim you posted an answer where a comment would be more appropriate.
Feb
27
comment Meeting management
Actually I wrote some code on Friday that attempted to generate a solution randomly. It failed spectacularly. I suspect that this schedule is actually impossible, and maybe some structural analysis could prove it. For example, take "person" $v_1$ and a Monday schedule 1-6, 7-12, etc. For the next four days, $v_1$ will meet with 20 other people, and there are 54 available. $v_1$ can't meet with 5 people from any other group, because they would all have to be on different days, so $v_1$ meets with $\leq 4$ people from each other group...
Feb
25
comment Meeting management
For some reason I can't edit the question, but here goes: There are 60 people. On each of five days, the people are partitioned into ten groups of six for day-long meetings. Is it possible to find a set of five partitions such that no two people meet twice?
Feb
25
answered How to find central vertex in a graph?
Feb
22
comment Finding local patterns in a circular list
Sorry, I meant $O(1)$ time, and $(1-\epsilon)n$ nodes.
Feb
22
comment Finding local patterns in a circular list
Well, here is a vague set of sufficient conditions: - the pattern always holds somewhere on a circular list - the pattern always holds somewhere on a linear list with property $x$. - given a circular list or a linear list with property $x$, we can find, in $O(\plog n)$ time, a linear sublist with property $x$ containing at most $(1-\epsilon)$ of the nodes.
Feb
21
comment A k-1 edge connected k regular graph is matching covered
Yes, I just added the missing details. Additionally I originally said "stable set polytope" when I meant to say "perfect matching polytope". Hope this helps.
Feb
21
revised A k-1 edge connected k regular graph is matching covered
added 1113 characters in body
Jan
6
comment Algorithm for calculating the sum-of-squares distance of a rolling window from a given line function
So in other words, the line for $y$ is "glued to" the window, and you move the window along the $x$-axis?
Jan
6
comment Algorithm for calculating the sum-of-squares distance of a rolling window from a given line function
Can you use $\Theta(n)$ storage? Why not just make a queue of squares of differences. When you advance the window by 1, simply add the new square difference and subtract the square distance that disappears from the window. This is constant time per step once you spend $O(n)$ time setting up the initial window. Or do you mean that the window is moved to some position arbitrarily far away?
Dec
9
comment Characteristics of locally triangle-free graph
This is a comment instead of an answer since I omit so many details. It's fairly easy to see that $G$ can be any tree. Fix a root and lay out the tree in such a way that the angle between any two children of a vertex is very small. If you do this with increasingly small angles as you move away from the root, you can complete the triangulation using points on an arc very far away from the tree, so that the tree is at the centre of the circle containing the arc. I believe it should be straightforward to modify the construction so that $G$ can actually be any acyclic graph.
Nov
21
comment SWAT vs Rioters (cops vs robbers variant)
If it is no, then see what happens for chordal graphs, then graphs of bounded treewidth.
Nov
21
comment SWAT vs Rioters (cops vs robbers variant)
Just a few thoughts. First, it is probably best, at least to start, to insist that $S$ and $R$ are increasing functions. It seems like the graph should be SWAT-win if SWAT can eradicate the rioters given any initial configuration. Characterizing SWAT-win graphs in a very general way seems very difficult, so I would start with the obvious first steps: Trees, cycles, outerplanar graphs. Then a first question becomes: Given a weighted graph and initial numbers of SWAT/Rioters, can we determine if it is SWAT-win in polynomial time? I suspect the answer is no, but I'm not sure.
Nov
8
comment probability distribution of hitting nodes on a finite graph random walk
Also sometimes known as small world graphs.