Sublinear Space Algorithms for the Longest Common Substring Problem

Given $m$ documents of total length $n$, we consider the problem of finding a longest string common to at least $d \geq 2$ of the documents. This problem is known as the \emph{longest common substring (LCS) problem} and has a classic $O(n)$ space and $O(n)$ time solution (Weiner [FOCS'73], Hui [CPM'92]). However, the use of linear space is impractical in many applications. In this paper we show that for any trade-off parameter $1 \leq \tau \leq n$, the LCS problem can be solved in $O(\tau)$ space and $O(n^2/\tau)$ time, thus providing the first smooth deterministic time-space trade-off from constant to linear space. The result uses a new and very simple algorithm, which computes a $\tau$-additive approximation to the LCS in $O(n^2/\tau)$ time and $O(1)$ space. We also show a time-space trade-off lower bound for deterministic branching programs, which implies that any deterministic RAM algorithm solving the LCS problem on documents from a sufficiently large alphabet in $O(\tau)$ space must use $\Omega(n\sqrt{\log(n/(\tau\log n))/\log\log(n/(\tau\log n)})$ time.Comment: Accepted to 22nd European Symposium on Algorithm

Measuring the Propagation of Information in Partial Evaluation

We present the first measurement-based analysis of the information propagated by a partial evaluator. Our analysis is based on measuring implementations of string-matching algorithms, based on the observation that the sequence of character comparisons accurately reflects maintained information. Notably, we can easily prove matchers to be different and we show that they display more variety and finesse than previously believed. As a consequence, we are able to pinpoint differences and inaccuracies in many results previously considered equivalent. Our analysis includes a framework that lets us obtain string matchers - notably the family of Boyer-Moore algorithms - in a systematic formalism-independent way from a few information-propagation primitives. By leveraging the existing research in string matching, we show that the landscape of information propagation is non-trivial in the sense that small changes in information propagation may dramatically change the properties of the resulting string matchers. We thus expect that this work will prove useful as a test and feedback mechanism for information propagation in the development of advanced program transformations, such as GPC or Supercompilation

Data Leak Detection As a Service: Challenges and Solutions

We describe a network-based data-leak detection (DLD) technique, the main feature of which is that the detection does not require the data owner to reveal the content of the sensitive data. Instead, only a small amount of specialized digests are needed. Our technique – referred to as the fuzzy fingerprint – can be used to detect accidental data leaks due to human errors or application flaws. The privacy-preserving feature of our algorithms minimizes the exposure of sensitive data and enables the data owner to safely delegate the detection to others.We describe how cloud providers can offer their customers data-leak detection as an add-on service with strong privacy guarantees. We perform extensive experimental evaluation on the privacy, efficiency, accuracy and noise tolerance of our techniques. Our evaluation results under various data-leak scenarios and setups show that our method can support accurate detection with very small number of false alarms, even when the presentation of the data has been transformed. It also indicates that the detection accuracy does not degrade when partial digests are used. We further provide a quantifiable method to measure the privacy guarantee offered by our fuzzy fingerprint framework