Quantum Algorithms for the Shortest Common Superstring and Text Assembling Problems

• URL: http://arxiv.org/abs/2306.10572v2
• Date: Sun, 31 Dec 2023 18:12:03 GMT
• Title: Quantum Algorithms for the Shortest Common Superstring and Text Assembling Problems
• Authors: Kamil Khadiev, Carlos Manuel Bosch Machado, Zeyu Chen, Junde Wu
• Abstract summary: We consider two versions of the Text Assembling problem. We are given a sequence of strings $s1,dots,sn$ of total length $L$ that is a dictionary, and a string $t$ of length $m$ that is texts. For both problems, we suggest new quantum algorithms that work better than their classical counterparts.
• Score: 11.048346250166073
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we consider two versions of the Text Assembling problem. We are given a sequence of strings $s^1,\dots,s^n$ of total length $L$ that is a dictionary, and a string $t$ of length $m$ that is texts. The first version of the problem is assembling $t$ from the dictionary. The second version is the ``Shortest Superstring Problem''(SSP) or the ``Shortest Common Superstring Problem''(SCS). In this case, $t$ is not given, and we should construct the shortest string (we call it superstring) that contains each string from the given sequence as a substring. These problems are connected with the sequence assembly method for reconstructing a long DNA sequence from small fragments. For both problems, we suggest new quantum algorithms that work better than their classical counterparts. In the first case, we present a quantum algorithm with $O(m+\log m\sqrt{nL})$ running time. In the case of SSP, we present a quantum algorithm with running time $O(n^3 1.728^n +L +\sqrt{L}n^{1.5}+\sqrt{L}n\log^2L\log^2n)$.

Related papers

• Efficient Algorithms for Recognizing Weighted Tree-Adjoining Languages [104.90415092306219]
  Four formalisms are equivalent to tree-adjoining grammars (TAG), linear indexed grammars (LIG), pushdown-adjoining automata (PAA) and embedded pushdown automata (EPDA) We design new algorithms for computing their stringsum derivations (the weight of all automatons of a string) and allsums (the weight of all derivations) For EPDA, our algorithm is both more space-efficient and time-efficient than the algorithm of Alonso et al. (2001) by factors of $mathcalO(|Gamma|2)$ and $
  arXiv  Detail & Related papers  (2023-10-23T18:26:00Z)
• A sublinear time quantum algorithm for longest common substring problem between run-length encoded strings [0.951828574518325]
  We give a sublinear quantum algorithm for the longest common (LCS) problem on the run-length encoded (RLE) inputs. Our algorithm costs $tildeO(n5/6)cdot O(mathrmpolylog(tilden))$ time, where $n$ and $tilden$ are the encoded and decoded length of the inputs, respectively.
  arXiv  Detail & Related papers  (2023-10-02T08:14:34Z)
• Mind the gap: Achieving a super-Grover quantum speedup by jumping to the end [114.3957763744719]
  We present a quantum algorithm that has rigorous runtime guarantees for several families of binary optimization problems. We show that the algorithm finds the optimal solution in time $O*(2(0.5-c)n)$ for an $n$-independent constant $c$. We also show that for a large fraction of random instances from the $k$-spin model and for any fully satisfiable or slightly frustrated $k$-CSP formula, statement (a) is the case.
  arXiv  Detail & Related papers  (2022-12-03T02:45:23Z)
• Quantum Resources Required to Block-Encode a Matrix of Classical Data [56.508135743727934]
  We provide circuit-level implementations and resource estimates for several methods of block-encoding a dense $Ntimes N$ matrix of classical data to precision $epsilon$. We examine resource tradeoffs between the different approaches and explore implementations of two separate models of quantum random access memory (QRAM) Our results go beyond simple query complexity and provide a clear picture into the resource costs when large amounts of classical data are assumed to be accessible to quantum algorithms.
  arXiv  Detail & Related papers  (2022-06-07T18:00:01Z)
• Exponential Separation between Quantum and Classical Ordered Binary Decision Diagrams, Reordering Method and Hierarchies [68.93512627479197]
  We study quantum Ordered Binary Decision Diagrams($OBDD$) model. We prove lower bounds and upper bounds for OBDD with arbitrary order of input variables. We extend hierarchy for read$k$-times Ordered Binary Decision Diagrams ($k$-OBDD$) of width.
  arXiv  Detail & Related papers  (2022-04-22T12:37:56Z)
• Quantum Algorithm for the Shortest Superstring Problem [0.0]
  We consider the Shortest Superstring Problem''(SSP) or the Shortest Common Superstring Problem''(SCS)
  arXiv  Detail & Related papers  (2021-12-26T05:37:56Z)
• Near-Optimal Quantum Algorithms for String Problems [0.5736353542430439]
  We give quantum algorithms for fundamental string problems with near-optimal query complexities and time complexities. These problems include Longest Common Substring, Lexicographically Minimal String Rotation, and Longest Square Substring. Our techniques naturally extend to other related string problems, such as Longest Repeated Substring, Longest Lyndon Substring, and Minimal Suffix.
  arXiv  Detail & Related papers  (2021-10-19T02:32:18Z)
• Quantum Algorithms for String Processing [58.720142291102135]
  We provide a quantum algorithm for the String matching problem that uses exponentially less quantum memory than existing ones. Using the same ideas, we provide two algorithms for the String comparing problem. The second algorithm works exponentially faster than the existing one.
  arXiv  Detail & Related papers  (2020-12-01T09:59:06Z)
• Quantum Meets Fine-grained Complexity: Sublinear Time Quantum Algorithms for String Problems [5.490993287665715]
  Longest common (LCS), longest palindrome (LPS), and Ulam distance (UL) are three fundamental string problems that can be classically solved in near linear time. We present sublinear time quantum algorithms for these problems along with quantum lower bounds.
  arXiv  Detail & Related papers  (2020-10-23T01:00:50Z)
• An Optimal Separation of Randomized and Quantum Query Complexity [67.19751155411075]
  We prove that for every decision tree, the absolute values of the Fourier coefficients of a given order $ellsqrtbinomdell (1+log n)ell-1,$ sum to at most $cellsqrtbinomdell (1+log n)ell-1,$ where $n$ is the number of variables, $d$ is the tree depth, and $c>0$ is an absolute constant.
  arXiv  Detail & Related papers  (2020-08-24T06:50:57Z)
• Classical and Quantum Algorithms for Constructing Text from Dictionary Problem [0.0]
  We study algorithms for solving the problem of constructing a text from a dictionary (sequence of small strings) The problem has an application in bioinformatics and has a connection with the Sequence assembly method for reconstructing a long DNA sequence from small fragments.
  arXiv  Detail & Related papers  (2020-05-28T22:44:01Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.