As probabilistic data structures are widely adopted in computing systems, their privacy is a major issue. Recent works have shown that even though the values stored in these structures look random, information can be extracted from them in some settings. In this paper, we consider the privacy of adaptive cuckoo filters, a probabilistic data structure that implements approximate membership checking. The main novelty and benefit of these filters are that they can adapt to removing false-positives. Unfortunately, our analysis shows that adaptation can dramatically reduce the privacy of the filters, allowing an attacker to extract the set of elements stored in the filter. Indeed, in some settings, the attacker can identify 100% of the elements stored in the filter. This means that the protection of the privacy of adaptive cuckoo filters should be considered. To that end, we propose preprocessing reduction (PR), a scheme that prevents an attacker from extracting the set of elements stored in the filter at the cost of increasing the false-positive probability of the filter. In many settings, the impact on false-positives will be negligible. For example, in a case study with 32-bit universes, the increase in the false-positive probability was smaller than 8% in all the configurations tested. Interestingly, PR is applicable not only to adaptive filters but also to approximate membership check filters in general and thus can be used to protect, for example, Bloom filters.

In network monitoring applications, it is often beneficial to employ a fast approximate set-membership filter to check if a given packet belongs to a monitored flow. Recent adaptive filter designs, such as the Adaptive Cuckoo Filter, are especially promising for such use cases as they adapt fingerprints to eliminate recurring false positives. In many traffic monitoring applications, it is also of interest to know the number of distinct flows that traverse a link or the number of nodes that are sending traffic. This is commonly done using cardinality estimation sketches. Therefore, on a given switch or network device, the same packets are typically processed using both a filter and a cardinality estimator. Having to process each packet with two independent data structures adds complexity to the implementation and limits performance. This paper shows that adaptive cuckoo filters can also be used to estimate the number of distinct negative elements queried on the filter. In flow monitoring, those distinct queries correspond to distinct flows. This is interesting as we get the cardinality estimation for free as part of the normal adaptive filter’s operation. We provide (1) a theoretical analysis, (2) simulation results, and (3) an evaluation with real packet traces to show that adaptive cuckoo filters can accurately estimate a wide range of cardinalities in practical scenarios.

Abstract Popular approximate membership query structures such as Bloom filters and cuckoo filters are widely used in databases, security, and networking. These structures represent sets approximately, and support at least two operations—insert and lookup; lookup always returns true on elements in the structure; it also returns true with some probability on elements not in the structure. These latter elements are called false positives. Compensatory for these false positives, filters can be much smaller than hash tables that represent the same set. However, unlike hash tables, cuckoo filters, and Bloom filters must be initialized with the intended number of maximum entries, and cannot grow larger—inserts beyond this number fail or significantly increase the false positive probability. This article presents designs and implementations of filters than can grow without inserts failing and without meaningfully increasing the false positive probability, even if the filters are created with a small initial size. The resulting code is available on GitHub under a permissive open source license.

The Green Driver app is a dynamic routing application for GPS-enabled smartphones. Green Driver combines client GPS data with real-time traffic light information provided by cities to determine optimal routes in response to driver route requests. Routes are optimized with respect to travel time, with the intention of saving the driver both time and fuel, and rerouting can occur if warranted. During a routing session, client phones communicate with a centralized server that both collects GPS data and processes route requests. All relevant data are anonymized and saved to databases for analysis; statistics are calculated from the aggregate data and fed back to the routing engine to improve future routing. Analyses can also be performed to discern driver trends: where do drivers tend to go, how long do they stay, when and where does traffic congestion occur, and so on. The system uses a number of techniques from the field of artificial intelligence. We apply a variant of A* search for solving the stochastic shortest path problem in order to find optimal driving routes through a network of roads given light-status information. We also use dynamic programming and hidden Markov models to determine the progress of a driver through a network of roads from GPS data and light-status data. The Green Driver system is currently deployed for testing in Eugene, Oregon, and is scheduled for large-scale deployment in Portland, Oregon, in Spring 2011.

A tanglegram is a pair of trees on the same set of leaves with matching leaves in the two trees joined by an edge. Tanglegrams are widely used in biology--to compare evolutionary histories of host and parasite species and to analyze genes of species in the same geographical area. We consider optimization problems in tanglegram drawings. We show a linear time algorithm to decide if a tanglegram admits a planar embedding by a reduction to the planar graph drawing problem. This problem was also studied by Fernau et al. A similar reduction to a graph crossing problem also helps to solve an open problem they posed, showing a fixed-parameter tractable algorithm for minimizing the number of crossings over all d-ary trees. For the case where one tree is fixed, we show an O(n log n) algorithm to determine the drawing of the second tree that minimizes the number of crossings. This improves the bound from earlier methods. We introduce a new optimization criterion using Spearman's footrule distance and give an O(n²) algorithm. We also show integer programming formulations to quickly obtain tanglegram drawings that minimize the two optimization measures discussed. We prove lower bounds on the maximum gap between the optimal solution and the heuristic of Dwyer and Schreiber to minimize crossings.