The ALENEX invited talk today was on routing problems. Rolf Mohring from TU Berlin presented a pair of case studies of routing problems in the "wild".
The following video explains the first case study:
Actually, the problem he was looking at was a tad simpler: you have containers coming in at Hamburg port, and you have automated robot vehicles that ferry the containers from the loading dock to their temporary storage locations. The problem is to create routes for the vehicles (on the fly) so that they reach their destination at a reasonable time without colliding with each other.
The actual solution involved successive shortest paths on a "time-expanded" flow graph, which in their case was a relatively simple grid graph. The time expansion refers to the fact that an "edge" is occupied between two time instants, and of course travel is blocked on an edge when it's occupied.
The second application, which in my mind was more impressive, was an instance of large-scale optimization to redesign the Berlin subway system. Perhaps the most impressive aspect of this work was that it's actually being used ! The latest incarnation of the Berlin subway schedule uses the schedule designed by their scheme, and the speaker showed a neat 4 minute Numb3rs-style video at the end targeting the layman that explained their work.
This is a tremendous achievement, both technically and politically. And I can't but wonder whether it's something about Germany itself, the home of classic engineering, that allows optimizations designed by researchers in a university to actually be implemented on a subway system. I'm probably wrong here, in that there must be numerous examples of success stories of OR in the US as well, but it does make me wonder.
Analysis: As examples of "applying algorithms in the real-world", the talk was great. As an example of the intricacies of doing "applied algorithms", it was less impressive: most of the "compromises with the real-world" were the same kinds of modifications to theoretical problems that one might expect to see in papers at ALENEX, and there was little takeaway to be had or lessons to be learned: I'd have loved to hear about how exactly they were able to convince the Berlin subway authority to implement their schemes.
This was either planned, or a happy coincidence, but the ANALCO invited speaker was Don Knuth, just a few days after his 70th birthday. The title of his talk was 'Puzzling problems', and as befits a Knuth talk, it was a random collection of cute problems in combinatorics. He had promised 5 such, with an exponentially increasing amount of time spent on each successive problem, but he only got through three of them. David's already described them in more detail here; all I can say is that it was a typical Knuthian talk :)
And yes, there were talks ! One talk that I'll draw attention to is on the work by Coleman and Wirth on the feedback arc set problem on tournaments. Given a directed graph in which for each pair of vertices, there's a directed edge one way or the other (i.e a tournament graph), can we delete the fewest number of edges so that the resulting graph is a DAG ? One important application of this problem is for aggregating rankings. Think of all the non-bribed figure skating judges at a competition, each creating a ranking of the performers. How do we aggregate these rankings into a "consensus" ranking ?
What is interesting about this problem is that it relates closely to sorting algorithms. In a sense, you can think of the rank aggregation problem as attempting to "sort" the participants into a total order, much like we have with a sorting problem. An earlier paper by Ailon, Charikar and Newman showed that a quick-sort like heuristic actually achieves a 3-approximation to the optimal solution to the feedback arc set problem, and other local heuristics for feedback arc set can also be related to sorting algorithms (although the analog of insertion sort performs quite badly).
Mergesort has not been translated to this framework: it's not obvious (but not hopeless) to see how to reformulate mergesort as an algorithm for feedback arc set, and indeed one open question from the earlier Ailon et al paper is an analysis of the behaviour of a mergesort-like method.
That's all for today, folks ! Tomorrow the action starts in earnest...
- The hotel wireless works in the lecture rooms (!). It's also free. this must be a first...
- The location is great. The hotel is on Van Ness and there are tons of restaurants (and Peets) within a block, as well as a drugstore and a Whole Foods.
- The ALENEX business meeting was the shortest business meeting in recorded history: it took all of 5 minutes. I commend the organizers for their good taste, and can only hope that SODA emulates them.