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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. Furthermore, the optimal nested test plan offering this performance, however, was not obtained. In this paper, we establish the optimal nested test plan in a 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.

97 MATHEMATICS AND COMPUTING↗

A learning-based measurement framework for traffic matrix inference in software defined networks

Here, we propose an intelligent framework for Traffic Matrix (TM) inference in Software Defined Networks (SDN) where the Ternary Content Addressable Memory (TCAM) entries of switches are partitioned into two parts to: (1) effectively aggregate part of incoming flows for aggregate measurements, and (2) de-aggregate and directly measure the most informative flows for per-flow measurements. These measurements are then processed to effectively estimate the size of network flows. Under hard resource constraints of limited TCAM sizes, we show how to design the optimal and efficient-compressed flow aggregation matrices. We propose an optimal Multi-Armed Bandit (MAB) based algorithm to adaptively measure the most rewarding flows. We evaluate the performance of our framework using real traffic traces from different network environments and by considering two main applications: TM estimation and Heavy Hitter (HH) detection. Moreover, we have implemented a prototype of our framework in Mininet to demonstrate its effectiveness.

42 ENGINEERING↗

Timely Reporting of Heavy Hitters Using External Memory

Given an input stream S of size N, a Φ-heavy hitter is an item that occurs at least ΦN times in S. The problem of finding heavy-hitters is extensively studied in the database literature. In this work, we study a real-time heavy-hitters variant in which an element must be reported shortly after we see its T = Φ N-th occurrence (and hence it becomes a heavy hitter). We call this the Timely Event Detection (TED) Problem. The TED problem models the needs of many real-world monitoring systems, which demand accurate (i.e., no false negatives) and timely reporting of all events from large, high-speed streams with a low reporting threshold (high sensitivity). Like the classic heavy-hitters problem, solving the TED problem without false-positives requires large space (Ω (N) words). Thus in-RAM heavy-hitters algorithms typically sacrifice accuracy (i.e., allow false positives), sensitivity, or timeliness (i.e., use multiple passes). We show how to adapt heavy-hitters algorithms to external memory to solve the TED problem on large high-speed streams while guaranteeing accuracy, sensitivity, and timeliness. Our data structures are limited only by I/O-bandwidth (not latency) and support a tunable tradeoff between reporting delay and I/O overhead. With a small bounded reporting delay, our algorithms incur only a logarithmic I/O overhead. We implement and validate our data structures empirically using the Firehose streaming benchmark. Multi-threaded versions of our structures can scale to process 11M observations per second before becoming CPU bound. In comparison, a naive adaptation of the standard heavy-hitters algorithm to external memory would be limited by the storage device’s random I/O throughput, i.e., ≈100K observations per second.

97 MATHEMATICS AND COMPUTING↗