arXiv subjects

Roberto De Prisco

Publications and source records attributed to Roberto De Prisco.

4 recordsLinked to original sources

arXiv2025

Optimal Binary Variable-Length Codes with a Bounded Number of 1's per Codeword: Design, Analysis, and Applications

In this paper, we consider the problem of constructing optimal average-length binary codes under the constraint that each codeword must contain at most $D$ ones, where $D$ is a given input parameter. We provide an $O(n^2D)$-time complexity algorithm for the construction of such codes, where $n$ is the number of codewords. We also describe several scenarios where the need to design these kinds of codes naturally arises. We also provide a Kraft-like inequality for the existence of (optimal) variable-length binary codes, subject to the above-described constraint on the number of 1's in each codeword.

cs.IT↗

arXiv2025

A simple proof for generalized Fibonacci numbers with dying rabbits

We consider the generalized Fibonacci counting problem with rabbits that become fertile at age $f$ and die at age $d$, with $1<=f<=d$ and $d$ finite or infinite. We provide a simple proof, based exclusively on a counting argumentation, for a recursive formula that gives the $n$th generalized Fibonacci number as a function of at most 3 previous numbers. The formula generalizes both the original Fibonacci sequence, for $f=2$ and $d=\infty$ (or $f=1$ and $d=2$), and other Fibonacci-related sequences, such as the Padovan sequence, for $f=2$ and $d=3$, the Tribonacci, for $f=1$ and $d=3$, Tetranacci, for $f=1$ and $d=4$, and alike sequences, for $f=1$ and finite values of $d$.

math.HO↗

arXiv2025

Old and New Results on Alphabetic Codes

This comprehensive survey examines the field of alphabetic codes, tracing their development from the 1960s to the present day. We explore classical alphabetic codes and their variants, analyzing their properties and the underlying mathematical and algorithmic principles. The paper covers the fundamental relationship between alphabetic codes and comparison-based search procedures and their applications in data compression, routing, and testing. We review optimal alphabetic code construction algorithms, necessary and sufficient conditions for their existence, and upper bounds on the average code length of optimal alphabetic codes. The survey also discusses variations and generalizations of the classical problem of constructing minimum average length alphabetic codes. By elucidating both classical results and recent findings, this paper aims to serve as a valuable resource for researchers and students, concluding with promising future research directions in this still-active field.

cs.IT↗

arXiv2024

Bounds and Algorithms for Alphabetic Codes and Binary Search Trees

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, and we show that the obtained codes are not too far from being optimal. Moreover, we exploit our results on alphabetic codes to provide new bounds on the average cost of optimal binary search trees. Our results improve on the best-known bounds on the average cost of optimal binary search trees present in the literature.

cs.IT↗