Related papers: Worst-Case Optimal Adaptive Prefix Coding
Many data compressors regularly encode probability distributions for entropy coding - requiring minimal description length type of optimizations. Canonical prefix/Huffman coding usually just writes lengths of bit sequences, this way…
Permutation patterns and pattern avoidance have been intensively studied in combinatorics and computer science, going back at least to the seminal work of Knuth on stack-sorting (1968). Perhaps the most natural algorithmic question in this…
Given two strings $T$ and $S$ and a set of strings $P$, for each string $p \in P$, consider the unique substrings of $T$ that have $p$ as their prefix and $S$ as their suffix. Two problems then come to mind; the first problem being the…
We show that the Longest Common Prefix Array of a text collection of total size n on alphabet [1, {\sigma}] can be computed from the Burrows-Wheeler transformed collection in O(n log {\sigma}) time using o(n log {\sigma}) bits of working…
We present the first worst-case linear time algorithm that directly computes the parameterized suffix and LCP arrays for constant sized alphabets. Previous algorithms either required quadratic time or the parameterized suffix tree to be…
In this paper, we revisit the classical data compression problem for domain specific texts. It is well-known that classical Huffman algorithm is optimal with respect to prefix encoding and the compression is done at character level. Since…
Two recent lower bounds on the compressibility of repetitive sequences, $\delta \le \gamma$, have received much attention. It has been shown that a length-$n$ string $S$ over an alphabet of size $\sigma$ can be represented within the…
A $\textit{compression scheme}$ $A$ for a class $\mathbb{G}$ of graphs consists of an encoding algorithm $\textit{Encode}_A$ that computes a binary string $\textit{Code}_A(G)$ for any given graph $G$ in $\mathbb{G}$ and a decoding algorithm…
Adaptive coding faces the following problem: given a collection of source classes such that each class in the collection has non-trivial minimax redundancy rate, can we design a single code which is asymptotically minimax over each class in…
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…
In the problem of compressive phase retrieval, one wants to recover an approximately $k$-sparse signal $x \in \mathbb{C}^n$, given the magnitudes of the entries of $\Phi x$, where $\Phi \in \mathbb{C}^{m \times n}$. This problem has…
In the dynamic minimum set cover problem, a challenge is to minimize the update time while guaranteeing close to the optimal $\min(O(\log n), f)$ approximation factor. (Throughout, $m$, $n$, $f$, and $C$ are parameters denoting the maximum…
Compressed Counting (CC) [22] was recently proposed for estimating the ath frequency moments of data streams, where 0 < a <= 2. CC can be used for estimating Shannon entropy, which can be approximated by certain functions of the ath…
For a packet erasure broadcast channel with three receivers, we propose a new coding algorithm that makes use of feedback to dynamically adapt the code. Our algorithm is throughput optimal, and we conjecture that it also achieves an…
Adaptive codes associate variable-length codewords to symbols being encoded depending on the previous symbols in the input data string. This class of codes has been introduced in [Dragos Trinca, cs.DS/0505007] as a new class of non-standard…
In this paper, we study the problem of designing prefix-free encoding schemes having minimum average code length that can be decoded efficiently under a decode cost model that captures memory hierarchy induced cost functions. We also study…
The dynamic set cover problem has been subject to growing research attention in recent years. In this problem, we are given as input a dynamic universe of at most $n$ elements and a fixed collection of $m$ sets, where each element appears…
This paper presents new lower and upper bounds for the optimal compression of binary prefix codes in terms of the most probable input symbol, where compression efficiency is determined by the nonlinear codeword length objective of…
In-place associative integer sorting technique was proposed for integer lists which requires only constant amount of additional memory replacing bucket sort, distribution counting sort and address calculation sort family of algorithms.…
We revisit the problem of finding shortest unique substring (SUS) proposed recently by [6]. We propose an optimal $O(n)$ time and space algorithm that can find an SUS for every location of a string of size $n$. Our algorithm significantly…