Abstract
Motivated by the Steiner tree problem with minimum number of Steiner points and bounded edge-length in [4], we consider the problem of constructing specific subgraph with minimum number of length-bounded stock pieces (CSS-MSP, for short), which is defined as follows. In some constructing specific subgraph problem Q (CSS, for short), the objective is to choose a minimum-length subset of edges, such that these edges form a specific subgraph (such as a spanning tree or a Steiner tree). In the CSS-MSP problem Q′, these edges are further required to be cut from some stock pieces of length L, and the new objective, however, is to minimize the number of stock pieces of length L to construct all edges in such a specific subgraph.We obtain two main results. (1) Whenever the CSS problem Q can be approximated by an α-approximation algorithm (α≥1) (for the case α=1, the CSS problem Q is solved optimally by a polynomial-time exact algorithm), we design two approximation algorithms with performance ratios 2α and 7α4 to solve the CSS-MSP problem Q′; (2) In addition, when the problem Q is to find a minimum spanning tree, we present a 32-approximation algorithm and an APTAS to solve the problem Q′ of constructing spanning tree with minimum number of length-bounded stock pieces.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
