Constrained LCS: Hardness and Approximation

Gotthilf, Zvi; Hermelin, Danny; Lewenstein, Moshe

doi:10.1007/978-3-540-69068-9_24

Cited by 27 publications

(19 citation statements)

References 11 publications

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“…In general case, the constrained longest common subsequence problem is NP-hard [47]. However, in our approach, we consider only some restriction of the problem that can be solved in polynomial time.…”

Section: Rfysmentioning

confidence: 99%

The Problem of Human-following for a Mobile Robot

Gorbenko¹

2018

KEG

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The problem of human-following for mobile robotic systems have been extensively studied. There are a number of approaches for different types of robots and sensor systems. In particular, different equipment of the environment and sensor-based methods by using a special suit have been applied for solution of the problem of human-following for mobile robots. This paper proposes an algorithm for the problem of human-following in an unequipped indoor environment for a low-cost mobile robot with a single visual sensor. We consider the results of computational experiments.Also, we consider the results of robotic experiments for day and night navigation.

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Section: Rfysmentioning

confidence: 99%

The Problem of Human-following for a Mobile Robot

Gorbenko¹

2018

KEG

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“…In the latter case, notice that C-LCS cannot be approximated, since a feasible solution for the C-LCS problem must be a supersequence of all the strings in the constraint C s and computing if such a feasible solution exists is NP-complete [8].…”

Section: Problem 1 Constrained Longest Common Subsequence (C-lcs)mentioning

confidence: 99%

Variants of constrained longest common subsequence

Bonizzoni

Vedova

Dondi

et al. 2010

Information Processing Letters

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In this work, we consider a variant of the classical Longest Common Subsequence problem called Doubly-Constrained Longest Common Subsequence (DC-LCS). Given two strings s 1 and s 2 over an alphabet Σ, a set C s of strings, and a function C o : Σ → N , the DC-LCS problem consists in finding the longest subsequence s of s 1 and s 2 such that s is a supersequence of all the strings in C s and such that the number of occurrences in s of each symbol σ ∈ Σ is upper bounded by C o (σ). The DC-LCS problem provides a clear mathematical formulation of a sequence comparison problem in Computational Biology and generalizes two other constrained variants of the LCS problem: the Constrained LCS and the Repetition-Free LCS. We present two results for the DC-LCS problem. First, we illustrate a fixed-parameter algorithm where the parameter is the length of the solution. Secondly, we prove a parameterized hardness result for the Constrained LCS problem when the parameter is the number of the constraint strings (|C s |) and the size of the alphabet Σ. This hardness result also implies the parameterized hardness of the DC-LCS problem (with the same parameters) and its NP-hardness when the size of the alphabet is constant.

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“…Very recently, two subcubic time algorithms for the SEQ-EC-LCS(2, 1) problem have been proposed by Deorowicz et al [14]. Gotthilf et al [19] have given a polynomial-time algorithm that approximates SEQ-IC-LCSðk; 1Þ within a factor of ffiffiffiffiffiffiffiffiffiffi ffi mjRj p , where m ¼ min 16i6L ðjS i jÞ. Gotthilf et al [18] also have studied the SEQ-EC-LCSðL; 'Þ problem.…”

Section: Introductionmentioning

confidence: 98%