Fully dynamic data structure for LCE queries in compressed space

A Longest Common Extension (LCE) query on a text $T$ of length $N$ asks for the length of the longest common prefix of suffixes starting at given two positions. We show that the signature encoding $\mathcal{G}$ of size $w = O(\min(z \log N \log^* M, N))$ [Mehlhorn et al., Algorithmica 17(2):183-198, 1997] of $T$, which can be seen as a compressed representation of $T$, has a capability to support LCE queries in $O(\log N + \log \ell \log^* M)$ time, where $\ell$ is the answer to the query, $z$ is the size of the Lempel-Ziv77 (LZ77) factorization of $T$, and $M \geq 4N$ is an integer that can be handled in constant time under word RAM model. In compressed space, this is the fastest deterministic LCE data structure in many cases. Moreover, $\mathcal{G}$ can be enhanced to support efficient update operations: After processing $\mathcal{G}$ in $O(w f_{\mathcal{A}})$ time, we can insert/delete any (sub)string of length $y$ into/from an arbitrary position of $T$ in $O((y+ \log N\log^* M) f_{\mathcal{A}})$ time, where $f_{\mathcal{A}} = O(\min \{ \frac{\log\log M \log\log w}{\log\log\log M}, \sqrt{\frac{\log w}{\log\log w}} \})$. This yields the first fully dynamic LCE data structure. We also present efficient construction algorithms from various types of inputs: We can construct $\mathcal{G}$ in $O(N f_{\mathcal{A}})$ time from uncompressed string $T$; in $O(n \log\log n \log N \log^* M)$ time from grammar-compressed string $T$ represented by a straight-line program of size $n$; and in $O(z f_{\mathcal{A}} \log N \log^* M)$ time from LZ77-compressed string $T$ with $z$ factors. On top of the above contributions, we show several applications of our data structures which improve previous best known results on grammar-compressed string processing.Comment: arXiv admin note: text overlap with arXiv:1504.0695

Dictionary matching in a stream

We consider the problem of dictionary matching in a stream. Given a set of strings, known as a dictionary, and a stream of characters arriving one at a time, the task is to report each time some string in our dictionary occurs in the stream. We present a randomised algorithm which takes O(log log(k + m)) time per arriving character and uses O(k log m) words of space, where k is the number of strings in the dictionary and m is the length of the longest string in the dictionary

Improved shape-signature and matching methods for model-based robotic vision

Researchers describe new techniques for curve matching and model-based object recognition, which are based on the notion of shape-signature. The signature which researchers use is an approximation of pointwise curvature. Described here is curve matching algorithm which generalizes a previous algorithm which was developed using this signature, allowing improvement and generalization of a previous model-based object recognition scheme. The results and the experiments described relate to 2-D images. However, natural extensions to the 3-D case exist and are being developed

Polygraph: Automatically generating signatures for polymorphic worms

It is widely believed that content-signature-based intrusion detection systems (IDSes) are easily evaded by polymorphic worms, which vary their payload on every infection attempt. In this paper, we present Polygraph, a signature generation system that successfully produces signatures that match polymorphic worms. Polygraph generates signatures that consist of multiple disjoint content sub-strings. In doing so, Polygraph leverages our insight that for a real-world exploit to function properly, multiple invariant substrings must often be present in all variants of a payload; these substrings typically correspond to protocol framing, return addresses, and in some cases, poorly obfuscated code. We contribute a definition of the polymorphic signature generation problem; propose classes of signature suited for matching polymorphic worm payloads; and present algorithms for automatic generation of signatures in these classes. Our evaluation of these algorithms on a range of polymorphic worms demonstrates that Polygraph produces signatures for polymorphic worms that exhibit low false negatives and false positives. © 2005 IEEE