Understanding a network's temporal evolution appears to require multiple observations of the graph over time. These often expensive repeated crawls are only able to answer questions about what happened from observation to observation, and not what happened before or between network snapshots. Contrary to this picture, we propose a method for Twitter's social network that takes a single static snapshot of network edges and user account creation times to accurately infer when these edges were formed. This method can be exact in theory, and we demonstrate empirically for a large subset of Twitter relationships that it is accurate to within a few hours in practice.

We discuss an online learning framework in which the agent is allowed to say I don't know'' as well as making incorrect predictions on given examples. We analyze the trade off between sayingI don't know'' and making mistakes. If the number of don't know predictions is forced to be zero, the model reduces to the well-known mistake-bound model introduced by Littlestone [Lit88]. On the other hand, if no mistakes are allowed, the model reduces to KWIK framework introduced by Li et. al. [LLW08]. We propose a general, though inefficient, algorithm for general finite concept classes that minimizes the number of don't-know predictions if a certain number of mistakes are allowed. We then present specific polynomial-time algorithms for the concept classes of monotone disjunctions and linear separators.

When online ads are shown together, they compete for user attention and conversions, imposing negative externalities on each other. While the competition for user attention in sponsored search can be captured via models of clickthrough rates, the post-click competition for conversions cannot: since the value-per-click of an advertiser is proportional to the conversion probability conditional on a click, which depends on the other ads displayed, the private value of an advertiser is no longer one-dimensional, and the GSP mechanism is not adequately expressive. We study the design of expressive GSP-like mechanisms for the simplest form that an advertiser's private value can have in the presence of such externalities- an advertiser's value depends on exclusivity, i.e., whether her ad is shown exclusively, or along with other ads.

We give approximation algorithms and inapproximability results for a class of movement problems. In general, these problems involve planning the coordinated motion of a large collection of objects (representing anything from a robot swarm or firefighter team to map labels or network messages) to achieve a global property of the network while minimizing the maximum or average movement. In particular, we consider the goals of achieving connectivity (undirected and directed), achieving connectivity between a given pair of vertices, achieving independence (a dispersion problem), and achieving a perfect matching (with applications to multicasting). This general family of movement problems encompasses an intriguing range of graph and geometric algorithms, with several real-world applications and a surprising range of approximability. In some cases, we obtain tight approximation and inapproximability results using direct techniques (without use of PCP), assuming just that P ≠ NP.

This paper considers scheduling tasks while minimizing the power consumption of one or more processors, each of which can go to sleep at a fixed cost α. There are two natural versions of this problem, both considered extensively in recent work: minimize the total power consumption (including computation time), or minimize the number of gaps in execution. For both versions in a multiprocessor system, we develop a polynomial-time algorithm based on sophisticated dynamic programming. In a generalization of the power-saving problem, where each task can execute in any of a specified set of time intervals, we develop a (1 + 23 α)-approximation, and show that dependence on α is necessary. In contrast, the analogous multi-interval gap scheduling problem is set-cover hard (and thus not o(lg n)-approximable), even in the special cases of just two intervals per job or just three unit intervals per job. We also prove several other hardness-of-approximation results. Finally, we give an O(√n)-approximation for maximizing throughput given a hard upper bound on the number of gaps.