Related papers: Optimal compression of hash-origin prefix trees
An optimal binary search tree for an access sequence on elements is a static tree that minimizes the total search cost. Constructing perfectly optimal binary search trees is expensive so the most efficient algorithms construct almost…
Most of the attention in statistical compression is given to the space used by the compressed sequence, a problem completely solved with optimal prefix codes. However, in many applications, the storage space used to represent the prefix…
Suppose we have n keys, n access probabilities for the keys, and n+1 access probabilities for the gaps between the keys. Let h_min(n) be the minimal height of a binary search tree for n keys. We consider the problem to construct an optimal…
We use a novel decomposition to create succinct data structures -- supporting a wide range of operations on static trees in constant time -- for a variety tree classes, extending results of Munro, Nicholson, Benkner, and Wild. Motivated by…
We present a compressed representation of tries based on top tree compression [ICALP 2013] that works on a standard, comparison-based, pointer machine model of computation and supports efficient prefix search queries. Namely, we show how to…
We present a new universal source code for distributions of unlabeled binary and ordinal trees that achieves optimal compression to within lower order terms for all tree sources covered by existing universal codes. At the same time, it…
An {\em ancestry labeling scheme} labels the nodes of any tree in such a way that ancestry queries between any two nodes in a tree can be answered just by looking at their corresponding labels. The common measure to evaluate the quality of…
In this work we study Invertible Bloom Lookup Tables (IBLTs) with small failure probabilities. IBLTs are highly versatile data structures that have found applications in set reconciliation protocols, error-correcting codes, and even the…
It is well-known that, given a probability distribution over $n$ characters, in the worst case it takes (\Theta (n \log n)) bits to store a prefix code with minimum expected codeword length. However, in this paper we first show that, for…
A new method for constructing minimum-redundancy binary prefix codes is described. Our method does not explicitly build a Huffman tree; instead it uses a property of optimal prefix codes to compute the codeword lengths corresponding to the…
We define simple variants of zip trees, called zip-zip trees, which provide several advantages over zip trees, including overcoming a bias that favors smaller keys over larger ones. We analyze zip-zip trees theoretically and empirically,…
Bytewise approximate matching algorithms have in recent years shown significant promise in de- tecting files that are similar at the byte level. This is very useful for digital forensic investigators, who are regularly faced with the…
Search trees are commonly used to implement access operations to a set of stored keys. If this set is static and the probabilities of membership queries are known in advance, then one can precompute an optimal search tree, namely one that…
We revisit the classical problem of designing optimally efficient cryptographically secure hash functions. Hash functions are traditionally designed via applying modes of operation on primitives with smaller domains. The results of…
Non-uniquely decodable codes can be defined as the codes that cannot be uniquely decoded without additional disambiguation information. These are mainly the class of non-prefix-free codes, where a codeword can be a prefix of other(s), and…
Apriori Algorithm is one of the most important algorithm which is used to extract frequent itemsets from large database and get the association rule for discovering the knowledge. It basically requires two important things: minimum support…
In this paper we propose an index key compression scheme based on the notion of distinction bits by proving that the distinction bits of index keys are sufficient information to determine the sorted order of the index keys correctly. While…
A recent work shows how we can optimize a tree based mode of operation for a rate 1 hash function. In particular, an algorithm and a theorem are presented for selecting a good tree topology in order to optimize both the running time and the…
We investigate the distribution of the depth of a node containing a specific key or, equivalently, the number of steps needed to retrieve an item stored in a randomly grown binary search tree. Using a representation in terms of mixed and…
In this paper, we revisit one of the simplest problems in data structures: the task of inserting elements into an open-addressed hash table so that elements can later be retrieved with as few probes as possible. We show that, even without…