TY - GEN

T1 - Boundary labeling for rectangular diagrams

AU - Bose, Prosenjit

AU - Carmi, Paz

AU - Keil, J. Mark

AU - Mehrabi, Saeed

AU - Mondal, Debajyoti

N1 - Publisher Copyright:
© Prosenjit Bose, Paz Carmi, J. Mark Keil, Saeed Mehrabi, and Debajyoti Mondal.

PY - 2018/6/1

Y1 - 2018/6/1

N2 - Given a set of n points (sites) inside a rectangle R and n points (label locations or ports) on its boundary, a boundary labeling problem seeks ways of connecting every site to a distinct port while achieving di erent labeling aesthetics. We examine the scenario when the connecting lines (leaders) are drawn as axis-aligned polylines with few bends, every leader lies strictly inside R, no two leaders cross, and the sum of the lengths of all the leaders is minimized. In a k-sided boundary labeling problem, where 1 ≤ k ≤ 4, the label locations are located on the k consecutive sides of R. In this paper we develop an O(n3 log n)-time algorithm for 2-sided boundary labeling, where the leaders are restricted to have one bend. This improves the previously best known O(n8 log n)time algorithm of Kindermann et al. (Algorithmica, 76(1):225–258, 2016). We show the problem is polynomial-time solvable in more general settings such as when the ports are located on more than two sides of R, in the presence of obstacles, and even when the objective is to minimize the total number of bends. Our results improve the previous algorithms on boundary labeling with obstacles, as well as provide the first polynomial-time algorithms for minimizing the total leader length and number of bends for 3- and 4-sided boundary labeling. These results settle a number of open questions on the boundary labeling problems (Wol, Handbook of Graph Drawing, Chapter 23, Table 23.1, 2014).

AB - Given a set of n points (sites) inside a rectangle R and n points (label locations or ports) on its boundary, a boundary labeling problem seeks ways of connecting every site to a distinct port while achieving di erent labeling aesthetics. We examine the scenario when the connecting lines (leaders) are drawn as axis-aligned polylines with few bends, every leader lies strictly inside R, no two leaders cross, and the sum of the lengths of all the leaders is minimized. In a k-sided boundary labeling problem, where 1 ≤ k ≤ 4, the label locations are located on the k consecutive sides of R. In this paper we develop an O(n3 log n)-time algorithm for 2-sided boundary labeling, where the leaders are restricted to have one bend. This improves the previously best known O(n8 log n)time algorithm of Kindermann et al. (Algorithmica, 76(1):225–258, 2016). We show the problem is polynomial-time solvable in more general settings such as when the ports are located on more than two sides of R, in the presence of obstacles, and even when the objective is to minimize the total number of bends. Our results improve the previous algorithms on boundary labeling with obstacles, as well as provide the first polynomial-time algorithms for minimizing the total leader length and number of bends for 3- and 4-sided boundary labeling. These results settle a number of open questions on the boundary labeling problems (Wol, Handbook of Graph Drawing, Chapter 23, Table 23.1, 2014).

KW - Dynamic programming

KW - Outerstring graphs

KW - Phrases Boundary labeling

UR - http://www.scopus.com/inward/record.url?scp=85049032134&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.SWAT.2018.12

DO - 10.4230/LIPIcs.SWAT.2018.12

M3 - Conference contribution

AN - SCOPUS:85049032134

T3 - Leibniz International Proceedings in Informatics, LIPIcs

SP - 121

EP - 1214

BT - 16th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2018

A2 - Eppstein, David

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 16th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2018

Y2 - 18 June 2018 through 20 June 2018

ER -