arXiv subjects

Michael Itzhaki

Publications and source records attributed to Michael Itzhaki.

4 recordsLinked to original sources

arXiv2026

On Time-Memory Tradeoffs for Maximal Palindromes with Wildcards and $k$-Mismatches

This paper addresses the problem of identifying palindromic factors in texts that include wildcards -- special characters that match all others. These symbols challenge many classical algorithms, as numerous combinatorial properties are not satisfied in their presence. We apply existing wildcard-LCE techniques to obtain a continuous time-memory tradeoff, and present the first non-trivial linear-space algorithm for computing all maximal palindromes with wildcards, improving the best known time-memory product in certain parameter ranges. Our main results are algorithms to find and approximate all maximal palindromes in a given text. We also generalize both methods to the $k$-mismatches setting, with or without wildcards.

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arXiv2025

Asymptotically Optimal Representation of Palindromic Structure

We introduce an asymptotically optimal representation of the Manacher array of a string that supports constant-time access. The approach relies on the combinatorial properties of palindromes, yielding a compact yet efficient structure. This work fits within the broader study of compressed text indexing and highlights structural aspects of palindromic substrings that may inspire further algorithmic applications.

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arXiv2025

Combinatorics of Palindromes

We investigate the structure and reconstruction complexity of Manacher arrays. First, we establish a combinatorial lower bound, proving that the number of rooted tandem repeat trees with $n+1$ genes exceeds the number of distinct Manacher arrays of length $n$. Second, we introduce a graph-theoretic framework that associates a graph to each Manacher array, where every proper vertex coloring yields a string consistent with the array. Finally, we analyze a reconstruction algorithm by I et al. (SPIRE 2010), showing that it simultaneously achieves a globally minimal alphabet size, uses at most $\log_2(n{-}1) + 2$ distinct symbols, and can be adapted to produce reconstructions over arbitrary alphabets when possible. Our results also resolve an open problem posed by the original authors. Together, these findings advance the combinatorial understanding of Manacher arrays and open new directions for string reconstruction under structural constraints.

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arXiv2024

Explicit Combinatoric Structures of Palindromes and Chromatic Number of Restriction Graphs

The palindromic fingerprint of a string $S[1\ldots n]$ is the set $PF(S) = \{(i,j)~|~ S[i\ldots j] \textit{ is a maximal }\\ \textit{palindrome substring of } S\}$. In this work, we consider the problem of string reconstruction from a palindromic fingerprint. That is, given an input set of pairs $PF \subseteq [1\ldots n] \times [1\ldots n]$ for an integer $n$, we wish to determine if $PF$ is a valid palindromic fingerprint for a string $S$, and if it is, output a string $S$ such that $PF= PF(S)$. I et al. [SPIRE2010] showed a linear reconstruction algorithm from a palindromic fingerprint that outputs the lexicographically smallest string over a minimum alphabet. They also presented an upper bound of $\mathcal{O}(\log(n))$ for the maximal number of characters in the minimal alphabet. In this paper, we show tight combinatorial bounds for the palindromic fingerprint reconstruction problem. We present the string $S_k$, which is the shortest string whose fingerprint $PF(S_k)$ cannot be reconstructed using less than $k$ characters. The results additionally solve an open problem presented by I et al.

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