Editor’s note: This is another guest post from Amitabh Trehan.
Hello from SODA at Austin. First, a few questions as warmup exercise (It’s a theory conference!):
– If I blog about the conference (my second conference reporting), should I not get a Press card and full financial support from the organizers? 🙂
– If the proceedings are on disk only, should there be more (or less) electric points in the seminar rooms?
– A European friend asked me ‘Is continental breakfast supposed to be just a bowl of fruits and coffee? Which continent are they referring to’?
– How did Austin land up in the middle of Texas?
So, on to some reports now (before my editor cuts my writing for being mathematically imprecise!). Kudos to Austin: on Saturday, I got to watch a wonderful performance by the Austin symphonic Orchestra and violinist Nadja Salerno-Sonnenberg sitting in the very first row on a $5 student ticket, and today live blues at a downtown bar. The conference itself is big: there are 3 parallel sessions throughout the day from 9 am to almost 7 pm besides a plenary session and best paper presentation. Of course, I could only attend at most (n-2)/3 + 2 talks, where n was the total number of talks.
The best paper award has been given to Asadpour, Goemans, Madry, Gharan and Saberi’s paper An O(log n/ log log n)-approximation Algorithm for the Asymmetric Traveling Salesman Problem . This paper breaks the 28 year old Θ(log n) bound set by Frieze et al for the classic Asymmetric Travelling Salesman Problem (ATSP). To remind the reader, ATSP is the asymmetric version of the Traveling Salesman Problem (TSP) which is the problem of finding the minimum cost tour visiting each vertex at least once given a set V of n vertices, and a cost function c: V X V -> R+, and where for ATSP c(u,v) need not be equal to c(v,u). The technique they have used is similiar to the algorithm for the symmetric version by Christofides which gives a factor 3/2 approximation. At a very high level, this is to construct a special spanning tree, find minimum cost Eulerian augmentation of this tree, and shortcut the resulting Eulerian walk to get the result. The spanning tree is special in the sense that it is a thin tree. The algorithm uses Held-Karp Linear Programming (LP) relaxation and a thin tree is roughly defined with respect to the optimum solution x* of the relaxation as a spanning tree that, for every cut, contains a small multiple of the corresponding values of x* in the cut. Shayan Oveis Gharan. presenting the paper, highlighted as important the ideas of ‘thinness’ and that of maximum entropy: explicitly fix the desired combinatorial structure, and then maximize the randomness. Overall, a very nice paper.
The other talk I will briefly discuss is the plenary session talk by Cynthia Dwork on ‘Differential Privacy’. She called it ‘postmodern privacy data analysis’. From what little I know (which is not much) of postmodernism, this seems an apt analogy: the author is supposed to be much less important (or almost anonymous) as compared to the work of the author. The aim of differential privacy is not only important but urgent in our time: How to publicly release statistical information about a set of people without compromising the privacy of any individual. Identity thefts and the ease with which one can obtain personal information is now getting alarming. After giving a brief history of the problem and explaining the concepts of adjacent databases, epsilon-differential privacy, linkage attacks etc, she presented the new extensions of their work using the H1N1 epidemic as an example: Continual observation and Pan-privacy. Continual observation is the question of how one can analyze aggregate user information to monitor, say, regional health conditions, while maintaining differential privacy. Pan-privacy maintains the privacy of the database “inside and out” completely hiding the pattern or appearance; protecting against both announced (legal action, subpoenas etc) and unannounced intrusions. The pan-privacy density estimator, as it is called, is based on an idea from the social sciences called randomized response given by Warner in 1965. The idea was to do a coin toss while recording the response of a respondent in a survey and record the response according to the result of the toss and possible truthfulness of the respondent’s statement. As Cynthia showed in her last slide, there are many animals now in the differential privacy zoo!
Besides these, I attended some interesting talks in the day ranging from property testing to graph theory (minors etc) and algorithms about clique-width and kernels. There was also, as one participant called ‘the Kawarabayashi’ session which had four papers by Ken-ichi Kawarabayashi, one less than last year (as far as I know).
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