TMBF: Bloom filter algorithms of time-dependent multi bit-strings for incremental set

Set is widely used as a kind of basic data structure. However, when it is used for large scale data set the cost of storage, search and transport is overhead. The bloom filter uses a fixed size bit string to represent elements in a static set, which can reduce storage space and search cost that is a fixed constant. The time-space efficiency is achieved at the cost of a small probability of false positive in membership query. However, for many applications the space savings and locating time constantly outweigh this drawback. Dynamic bloom filter (DBF) can support concisely representation and approximate membership queries of dynamic set instead of static set. It has been proved that DBF not only possess the advantage of standard bloom filter, but also has better features when dealing with dynamic set. This paper proposes a time-dependent multiple bit-strings bloom filter (TMBF) which roots in the DBF and targets on dynamic incremental set. TMBF uses multiple bit-strings in time order to present a dynamic increasing set and uses backward searching to test whether an element is in a set. Based on the system logs from a real P2P file sharing system, the evaluation shows a 20% reduction in searching cost compared to DBF

Average-Case Optimal Approximate Circular String Matching

Approximate string matching is the problem of finding all factors of a text t of length n that are at a distance at most k from a pattern x of length m. Approximate circular string matching is the problem of finding all factors of t that are at a distance at most k from x or from any of its rotations. In this article, we present a new algorithm for approximate circular string matching under the edit distance model with optimal average-case search time O(n(k + log m)/m). Optimal average-case search time can also be achieved by the algorithms for multiple approximate string matching (Fredriksson and Navarro, 2004) using x and its rotations as the set of multiple patterns. Here we reduce the preprocessing time and space requirements compared to that approach

A practical index for approximate dictionary matching with few mismatches

Approximate dictionary matching is a classic string matching problem (checking if a query string occurs in a collection of strings) with applications in, e.g., spellchecking, online catalogs, geolocation, and web searchers. We present a surprisingly simple solution called a split index, which is based on the Dirichlet principle, for matching a keyword with few mismatches, and experimentally show that it offers competitive space-time tradeoffs. Our implementation in the C++ language is focused mostly on data compaction, which is beneficial for the search speed (e.g., by being cache friendly). We compare our solution with other algorithms and we show that it performs better for the Hamming distance. Query times in the order of 1 microsecond were reported for one mismatch for the dictionary size of a few megabytes on a medium-end PC. We also demonstrate that a basic compression technique consisting in $q$-gram substitution can significantly reduce the index size (up to 50% of the input text size for the DNA), while still keeping the query time relatively low