We consider the communication complexity of Hamming distance two strings. Bille et al. [SPIRE 2018] considered longest common prefix (LCP) problem in setting where parties have their strings a compressed form, i.e., represented by Lempel-Ziv 77 factorization (LZ77) with/without self-references. present randomized public-coin protocol for joint computation LZ77 without Although our scheme is hea...

Let x, y be strings of equal length. The Hamming distance h(x, y) between x and y is the number of positions in which x and y differ. If x is a cyclic shift of y, we say x and y are conjugates. We consider f(x, y), the Hamming distance between the conjugates xy and yx. Over a binary alphabet f(x, y) is always even, and must satisfy a further technical condition. By contrast, over an alphabet of...

Similarity search is crucial to many applications. Of particular interest are two flavors of the Hamming distance range query, namely, the Hamming select and the Hamming join (Hamming-select and Hamming-join, respectively). Hamming distance is widely used in approximate near neighbor search for high dimensional data, such as images and document collections. For example, using predefined similar...

Given a string x and a language L, the Hamming distance of x to L is the minimum Hamming distance of x to any string in L. The edit distance of a string to a language is analogously defined. First, we prove that there is a language in AC such that both Hamming and edit distance to this language are hard to approximate; they cannot be approximated with factor O(n 1 3 − ), for any > 0, unless P =...

Motivated by large-scale multimedia applications we propose to learn mappings from high-dimensional data to binary codes that preserve semantic similarity. Binary codes are well suited to large-scale applications as they are storage efficient and permit exact sub-linear kNN search. The framework is applicable to broad families of mappings, and uses a flexible form of triplet ranking loss. We ov...