Related papers: Reserved-Length Prefix Coding
Code Language Models have been trained to generate accurate solutions, typically with no regard for runtime. On the other hand, previous works that explored execution optimisation have observed corresponding drops in functional correctness.…
We propose a new class of space-time block codes based on finite-field rank-metric codes in combination with a rank-metric-preserving mapping to the set of Eisenstein integers. It is shown that these codes achieve maximum diversity order…
A new scheme for the problem of centralized coded caching with non-uniform demands is proposed. The distinguishing feature of the proposed placement strategy is that it admits equal sub-packetization for all files while allowing the users…
This letter investigates a new class of index coding problems. One sender broadcasts packets to multiple users, each desiring a subset, by exploiting prior knowledge of linear combinations of packets. We refer to this class of problems as…
We study the computational complexity of approximating general constrained Markov decision processes. Our primary contribution is the design of a polynomial time $(0,\epsilon)$-additive bicriteria approximation algorithm for finding optimal…
The problem of finding a center string that is `close' to every given string arises and has many applications in computational biology and coding theory. This problem has two versions: the Closest String problem and the Closest Substring…
Efficient methods for storing and querying are critical for scaling high-order n-gram language models to large corpora. We propose a language model based on compressed suffix trees, a representation that is highly compact and can be easily…
Nowadays there are several classes of constrained codes intended for different applications. The following two large classes can be distinguished. The first class contains codes with local constraints; for example, the source data must be…
Partitioning a sequence of length $n$ into $k$ coherent segments (Seg) is one of the classic optimization problems. As long as the optimization criterion is additive, Seg can be solved exactly in $O(n^2k)$ time using a classic dynamic…
A framework with two scalar parameters is introduced for various problems of finding a prefix code minimizing a coding penalty function. The framework encompasses problems previously proposed by Huffman, Campbell, Nath, and Drmota and…
In various applications the search for certificates for certain properties (e.g., stability of dynamical systems, program termination) can be formulated as a quantified constraint solving problem with quantifier prefix exists-forall. In…
This paper deals with a universal coding problem for a certain kind of multiterminal source coding network called a generalized complementary delivery network. In this network, messages from multiple correlated sources are jointly encoded,…
This paper addresses two central problems for probabilistic processing models: parameter estimation from incomplete data and efficient retrieval of most probable analyses. These questions have been answered satisfactorily only for…
Alphabetic codes and binary search trees are combinatorial structures that abstract search procedures in ordered sets endowed with probability distributions. In this paper, we design new linear-time algorithms to construct alphabetic codes,…
Codes for rank modulation have been recently proposed as a means of protecting flash memory devices from errors. We study basic coding theoretic problems for such codes, representing them as subsets of the set of permutations of $n$…
An index coding scheme in which the source (transmitter) transmits binary symbols over a wireless fading channel is considered. Index codes with the transmitter using minimum number of transmissions are known as optimal index codes.…
Prolog's ability to return multiple answers on backtracking provides an elegant mechanism to derive reversible encodings of combinatorial objects as Natural Numbers i.e. {\em ranking} and {\em unranking} functions. Starting from a…
We present two structural results concerning longest common prefixes of non-empty languages. First, we show that the longest common prefix of the language generated by a context-free grammar of size $N$ equals the longest common prefix of…
In the weighted flow-time problem on a single machine, we are given a set of n jobs, where each job has a processing requirement p_j, release date r_j and weight w_j. The goal is to find a preemptive schedule which minimizes the sum of…
We are given a set of $n$ jobs and a single processor that can vary its speed dynamically. Each job $J_j$ is characterized by its processing requirement (work) $p_j$, its release date $r_j$ and its deadline $d_j$. We are also given a budget…