A closest vector problem arising in radiation therapy planning
نویسندگان
چکیده
منابع مشابه
A closest vector problem arising in radiation therapy planning
In this paper we consider the problem of finding a vector that can be written as a nonnegative, integer and linear combination of given 0-1 vectors, the generators, such that the l1-distance between this vector and a given target vector is minimized. We prove that this closest vector problem is NP-hard to approximate within an additive error of (ln 2− ǫ)d ≈ (0, 693 − ǫ) d for all ǫ > 0 where d ...
متن کاملul 2 00 9 A closest vector problem arising in radiation therapy planning ∗
In this paper we consider the problem of finding a vector that can be written as a nonnegative, integer and linear combination of given 0-1 vectors, the generators, such that the l1-distance between this vector and a given target vector is minimized. We prove that this closest vector problem is NP-hard to approximate within an additive error of (ln 2− ǫ)d ≈ (0, 693 − ǫ) d for all ǫ > 0 where d ...
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The Closest Vector Problem (CVP) is a computational problem on lattices closely related to SVP. (See Shortest Vector Problem.) Given a lattice L and a target point ~x, CVP asks to find the lattice point closest to the target. As for SVP, CVP can be defined with respect to any norm, but the Euclidean norm is the most common (see the entry lattice for a definition). A more relaxed version of the ...
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The closest vector problem for general lattices is NP-hard. However, we can efficiently find the closest lattice points for some special lattices, such as root lattices (An, Dn and some En). In this paper, we discuss the closest vector problem on more general lattices than root lattices.
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We present a 2 O(n) time Turing reduction from the closest lattice vector problem to the shortest lattice vector problem. Our reduction assumes access to a subroutine that solves SVP exactly and a subroutine to sample short vectors from a lattice, and computes a (1+)-approximation to CVP. As a consequence, using the SVP algorithm from 1], we obtain a randomized 2 O(1+ ?1)n algorithm to obtain a...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Optimization
سال: 2010
ISSN: 1382-6905,1573-2886
DOI: 10.1007/s10878-010-9308-8