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
2001622826
This paper addresses the problem of noisy Generalized Binary Search (GBS). GBS is a well-known greedy algorithm for determining a binary-valued hypothesis through a sequence of strategically selected queries. At each step, a query is selected that most evenly splits the hypotheses under consideration into two disjoint subsets, a natural generalization of the idea underlying classic binary search. GBS is used in many applications, including fault testing, machine diagnostics, disease diagnosis, job scheduling, image processing, computer vision, and active learning. In most of these cases, the responses to queries can be noisy. Past work has provided a partial characterization of GBS, but existing noise-tolerant versions of GBS are suboptimal in terms of query complexity. This paper presents an optimal algorithm for noisy GBS and demonstrates its application to learning multidimensional threshold functions. This paper investigates the problem of determining a binary-valued function through a sequence of strategically selected queries. The focus is an algorithm called Generalized Binary Search (GBS). GBS is a well-known greedy algorithm for determining a binary-valued function through a sequence of strategically selected queries. At each step, a query is selected that most evenly splits the hypotheses under consideration into two disjoint subsets, a natural generalization of the idea underlying classic binary search. This paper develops novel incoherence and geometric conditions under which GBS achieves the information-theoretically optimal query complexity; i.e., given a collection of N hypotheses, GBS terminates with the correct function after no more than a constant times logN queries. Furthermore, a noise-tolerant version of GBS is developed that also achieves the optimal query complexity. These results are applied to learning halfspaces, a problem arising routinely in image processing and machine learning. A new technology evaluation of fingerprint verification algorithms has been organized following the approach of the previous FVC2000 and FVC2002 evaluations, with the aim of tracking the quickly evolving state-of-the-art of fingerprint recognition systems. Three sensors have been used for data collection, including a solid state sweeping sensor, and two optical sensors of different characteristics. The competition included a new category dedicated to ”light” systems, characterized by limited computational and storage resources. This paper summarizes the main activities of the FVC2004 organization and provides a first overview of the evaluation. Results will be further elaborated and officially presented at the International Conference on Biometric Authentication (Hong Kong) on July 2004. Citation analysis is performed to evaluate the impact of scientific collections (journals and conferences), publications and scholar authors. In this paper we investigate alternative methods to provide a generalized approach to rank scientific publications. We use the SCEAS system [12] as a base platform to introduce new methods that can be used for ranking scientific publications. Moreover, we tune our approach along the reasoning of the prizes 'VLDB 10 Year Award' and 'SIGMOD Test of Time Award', which have been awarded in the course of the top two database conferences. Our approach can be used to objectively suggest the publications and the respective authors the are more likely to be awarded in the near future at these conferences.