5,133 research outputs found
Active Learning of Multiple Source Multiple Destination Topologies
We consider the problem of inferring the topology of a network with
sources and receivers (hereafter referred to as an -by- 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., -by-'s or -by-'s) and then merge these components
to identify the -by- 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 -by- topology is given and that all
-by- components can be queried and learned using end-to-end probes. The
problem is which -by-'s to query and how to merge them with the given
-by-, so as to exactly identify the -by- 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, , on the number of
-by-'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 -by- 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 -by-, and
merges it with the given -by-; it requires exactly steps, which is
much less than all possible -by-'s. Simulation results
over synthetic and realistic topologies demonstrate that both algorithms
correctly identify the -by- topology and are near-optimal, but REA is
more efficient in practice
Optimal Nested Test Plan for Combinatorial Quantitative Group Testing
We consider the quantitative group testing problem where the objective is to
identify defective items in a given population based on results of tests
performed on subsets of the population. Under the quantitative group testing
model, the result of each test reveals the number of defective items in the
tested group. The minimum number of tests achievable by nested test plans was
established by Aigner and Schughart in 1985 within a minimax framework. The
optimal nested test plan offering this performance, however, was not obtained.
In this work, we establish the optimal nested test plan in closed form. This
optimal nested test plan is also order optimal among all test plans as the
population size approaches infinity. Using heavy-hitter detection as a case
study, we show via simulation examples orders of magnitude improvement of the
group testing approach over two prevailing sampling-based approaches in
detection accuracy and counter consumption. Other applications include anomaly
detection and wideband spectrum sensing in cognitive radio systems
- β¦