Elsevier

Information Processing Letters

Volume 65, Issue 4, 27 February 1998, Pages 201-207
Information Processing Letters

A polynomial time solution for labeling a rectilinear map

https://doi.org/10.1016/S0020-0190(98)00002-7Get rights and content

Abstract

Given a rectilinear map consisting of n disjoint line segments, the corresponding map labeling problem is to place a maximum width rectangle at each segment using one of the three natural ways. In a recent paper, it is shown that if all segments are horizontal then the problem can be solved in optimal Θ(n log n) time. For the general problem a factor-2 approximate solution and a Polynomial Time Approximation Scheme are also proposed. In this paper, we show that the general problem is polynomially solvable with a nontrivial use of 2SAT and the solution can be even generalized to the case of allowing k natural placements for each segment, where k is any fixed constant. We believe this technique can be also used to solve other geometric packing problems.

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This work is partially supported by the research grant No. 9030526 from City University of Hong Kong.

2

This work was done while he was visiting City University of Hong Kong and is also partially supported by the RGC grant (HKU 541/96E).

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