5 research outputs found

    Active Learning of Multiple Source Multiple Destination Topologies

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    We consider the problem of inferring the topology of a network with MM sources and NN receivers (hereafter referred to as an MM-by-NN 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 (i.e., 11-by-NN's or 22-by-22's) and then merge these components to identify the MM-by-NN topology. In this paper, we focus on the second part, which had previously received less attention in the literature. In particular, we assume that a 11-by-NN topology is given and that all 22-by-22 components can be queried and learned using end-to-end probes. The problem is which 22-by-22's to query and how to merge them with the given 11-by-NN, so as to exactly identify the 22-by-NN 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, N2\lceil \frac{N}{2} \rceil, on the number of 22-by-22'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), since our problem is one of active learning, from 22-by-22 queries. The second algorithm is called the Receiver Elimination Algorithm (REA) and follows a bottom-up approach: at every step, it selects two receivers, queries the corresponding 22-by-22, and merges it with the given 11-by-NN; it requires exactly N1N-1 steps, which is much less than all (N2)\binom{N}{2} possible 22-by-22's. Simulation results over synthetic and realistic topologies demonstrate that both algorithms correctly identify the 22-by-NN topology and are near-optimal, but REA is more efficient in practice
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