Machinations


Day 2 at SODA
January 19, 2010, 10:54 pm
Filed under: Uncategorized | Tags: , ,

Editor: Guest Post again by Amitabh Trehan

I am in the business meeting: surprisingly, it’s a lot of fun, maybe due to the free drinks and the humorous presentations by the contenders for SODA 2012,  freed, it seems, from the betas, thetas and hidden constants! Ok then, after multi-round voting by a show of hands and a play of non-musical chairs on a large scale (to help get the count correct), Kyoto has narrowly triumphed in it’s bid for 2012 over Barcelona: the other contenders (in order of votes received) were Prague, Rome and New York. There were some wild celebrations and tennis style fist-pumping!

There were many exciting talks today ranging from algorithmic game theory to distribued computing to graph algorithms and some indescribable topics like those at the business meeting!

Noam Nisan gave a very interesting talk on Google’s auction for tv ads.  I think I’ve been seeing the mention of this article on the blogosphere somewhere but avoided reading it (maybe I thought it was a google advert :). First, it was  indeed a surprise that Google markets television ads, but as it turns out, they have good reason to do so. Google brings a new system of marketing advertisement time that is different from the traditional office room deals, and which brings nice algorithmic challenges too. For the adverstisor, Google brings a web-based interface, precise targeting of content, and excellent feedback. The auctions are run everyday (for the next days advertisements, I think). Informally, the auction has slots for sale, bidders bid with their value for the particular slots and total budget, and the auction outputs the set of slots won by each bidder, and the price for which that slot is given.   The problem model is fairly straightforward with some simple constraints. The algorithm tries to optimize revenue, efficiency, and fairness.

The  auction is based on simultaneous ascending auction, and basically is as follows:  each ad-slot has an associated price that keeps increasing throughout the auction. Prices start at low reserve prices, and rise whenever there is “over-demand” for an ad-slot — i.e. a slot that is currently held
by one bidder is desired by another. Such small price increases keep going on until there is no
“over-demand”, at which point the auction closes. The basic step in the auction is the calculation
of the “demand” of a bidder at current prices — i.e. which set of slots would this bidder desire to
acquire assuming that slots are priced as given. In its basic form, the calculation of this demand is
done by a greedy algorithm that chooses slots according to decreasing bid-to-price ratio. Under certain theoretical assumptions (“gross substitutes”) it is known that this procedure ends with a “Walrasian market equilibrium” and under even stricter assumptions these prices are incentive compatible — i.e. they give no bidder any strategic reason to under or over bid.  In reality, some slots may go unsold though, and they are put through the wringer again till google is sure nobody wants them. At that point google puts up public service ads on them such as those asking people to desist from taking drugs. As Noam said, it’s not the case that google doesn’t want you to take drugs, it’s just that they have empty slots :); So, a betting hunch I have from this talk is that if you see too many public service ads coming on the television, maybe the slots are going cheap and it’s time to buy them!!!

I would like to briefly mention a few more talks here: Monotonicity in Bargaining Networks by Yossi Azar et al. talked about bargaining networks.  In these networks, the nodes are players, and each edge has a certain amount of money on it that can be split among the endpoints of that edge only if the endpoints reach an agreement on how to split the dollar.  However, each node is allowed to split the money with at most one neighbor.  There are many real world situations where such networks exist e.g. among buyers and sellers where the edge weight can be considered as the difference in value of the object being sold, and in dating or marriage, where the edge weight would relate to the benefit of a relationship. A stable solution is related to the fractional min cover and thereby, maximum matching.  The authors show that for several solution concepts (i.e. stable outcomes) for this game are monotonic on bipartite graphs, where monotonic means that adding an edge between nodes x and y can only increase the profit of x and y on the bargaining network.Interesting questions remain: What are the  mechanisms of bargaining? Are there simple distributed algorithms for these solutions? lower bounds?

The evening talks on A model of computation for map reduce, and Deterministic algorithms for the Lovasz local lemma drew much interest from the audience. I also enjoyed the talks Highwway dimension, shortest paths and provable efficient algos, and max flows in planar graphs.

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