We consider the problem of inferring the topology of a network with M sources and N receivers (an M-by- N network), by sending probes between the sources and receivers. Prior work has shown that this problem can be decomposed into two parts: first, infer smaller subnetwork components (1-by- N's or 2-by-2's) and then merge them to identify the M-by- N topology. We focus on the second part, which had previously received less attention in the literature. We assume that a 1-by- N topology is given and that all 2-by-2 components can be queried and learned using end-to-end probes. The problem is which 2-by-2's to query and how to merge them with the given 1-by- N, so as to exactly identify the 2-by- N topology, and optimize a number of performance metrics, including the number of queries (which directly translates into measurement bandwidth), time complexity, and memory usage. We provide a lower bound, [N 2], on the number of 2-by-2's required by any active learning algorithm and propose two greedy algorithms. The first algorithm follows the framework of multiple hypothesis testing, in particular Generalized Binary Search (GBS). The second algorithm is called the Receiver Elimination Algorithm (REA) and follows a bottom-up approach. It requires exactly N-1 steps, which is much less than all (2N) possible 2-by-2's. Simulation results demonstrate that both algorithms correctly identify the 2-by- N topology and are near-optimal, but REA is more efficient in practice.
Relation to the conference version. This journal paper builds on our conference paper in @cite_39 . In addition to revisions and elaborating on parts of the writing, new materials contributions in this paper include the following: the formulation of the problem in the GBS framework as well as the performance evaluation of the GBS algorithm via simulation, and its comparison against REA.
@cite_39
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We present a recommender systems approach to conference paper assignment, i.e., the task of assigning paper submissions to reviewers. We address both the modeling of reviewer-paper preferences (which can be cast as a learning problem) and the optimization of reviewing assignments to satisfy global conference criteria (which can be viewed as constraint satisfaction). Due to the paucity of preference data per reviewer or per paper (relative to other recommender systems applications) we show how we can integrate multiple sources of information to learn reviewer-paper preference models. Our models are evaluated not just in terms of prediction accuracy but in terms of end-assignment quality. Using a linear programming-based assignment optimization, we show how our approach better explores the space of unsupplied assignments to maximize the overall affinities of papers assigned to reviewers. We demonstrate our results on real reviewer bidding data from the IEEE ICDM 2007 conference.