An Exact Algorithm for the Arrow Placement Problem in Directed Graph Drawings
Summary :
We consider the problem of placing arrows, which indicate the direction of each edge in directed graph drawings, without making them overlap other arrows, vertices and edges as much as possible. The following two methods have been proposed for this problem. One is an exact algorithm for the case in which the position of each arrow is restricted to some discrete points. The other is a heuristic algorithm for the case in which the arrow is allowed to move continuously on each edge. In this paper, we assume that the arrow positions are not restricted to discrete points and propose an exact algorithm for the problem of finding an arrow placement such that (a) the weighted sum of the numbers of overlaps with edges, vertices and other arrows is minimized and (b) the sum of the distances between the arrows and their edges' terminal vertices is minimized as a secondary objective. The proposed method solves this problem by reducing it to a mixed integer linear programming problem. Since this is an exponential time algorithm, we add a simple procedure as preprocessing to reduce the running time. Experimental results show that the proposed method can find a better arrow placement than the previous methods and the procedure for reducing the running time is effective.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E102-A No.11 pp.1481-1489
- Publication Date
- 2019/11/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E102.A.1481
- Type of Manuscript
- PAPER
- Category
- Algorithms and Data Structures
Authors
Naoto KIDO
Kobe University
Sumio MASUDA
Kobe University
Kazuaki YAMAGUCHI
Kobe University
Keyword
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Naoto KIDO, Sumio MASUDA, Kazuaki YAMAGUCHI, "An Exact Algorithm for the Arrow Placement Problem in Directed Graph Drawings" in IEICE TRANSACTIONS on Fundamentals,
vol. E102-A, no. 11, pp. 1481-1489, November 2019, doi: 10.1587/transfun.E102.A.1481.
Abstract: We consider the problem of placing arrows, which indicate the direction of each edge in directed graph drawings, without making them overlap other arrows, vertices and edges as much as possible. The following two methods have been proposed for this problem. One is an exact algorithm for the case in which the position of each arrow is restricted to some discrete points. The other is a heuristic algorithm for the case in which the arrow is allowed to move continuously on each edge. In this paper, we assume that the arrow positions are not restricted to discrete points and propose an exact algorithm for the problem of finding an arrow placement such that (a) the weighted sum of the numbers of overlaps with edges, vertices and other arrows is minimized and (b) the sum of the distances between the arrows and their edges' terminal vertices is minimized as a secondary objective. The proposed method solves this problem by reducing it to a mixed integer linear programming problem. Since this is an exponential time algorithm, we add a simple procedure as preprocessing to reduce the running time. Experimental results show that the proposed method can find a better arrow placement than the previous methods and the procedure for reducing the running time is effective.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E102.A.1481/_p
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@ARTICLE{e102-a_11_1481,
author={Naoto KIDO, Sumio MASUDA, Kazuaki YAMAGUCHI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={An Exact Algorithm for the Arrow Placement Problem in Directed Graph Drawings},
year={2019},
volume={E102-A},
number={11},
pages={1481-1489},
abstract={We consider the problem of placing arrows, which indicate the direction of each edge in directed graph drawings, without making them overlap other arrows, vertices and edges as much as possible. The following two methods have been proposed for this problem. One is an exact algorithm for the case in which the position of each arrow is restricted to some discrete points. The other is a heuristic algorithm for the case in which the arrow is allowed to move continuously on each edge. In this paper, we assume that the arrow positions are not restricted to discrete points and propose an exact algorithm for the problem of finding an arrow placement such that (a) the weighted sum of the numbers of overlaps with edges, vertices and other arrows is minimized and (b) the sum of the distances between the arrows and their edges' terminal vertices is minimized as a secondary objective. The proposed method solves this problem by reducing it to a mixed integer linear programming problem. Since this is an exponential time algorithm, we add a simple procedure as preprocessing to reduce the running time. Experimental results show that the proposed method can find a better arrow placement than the previous methods and the procedure for reducing the running time is effective.},
keywords={},
doi={10.1587/transfun.E102.A.1481},
ISSN={1745-1337},
month={November},}
Copy
TY - JOUR
TI - An Exact Algorithm for the Arrow Placement Problem in Directed Graph Drawings
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1481
EP - 1489
AU - Naoto KIDO
AU - Sumio MASUDA
AU - Kazuaki YAMAGUCHI
PY - 2019
DO - 10.1587/transfun.E102.A.1481
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E102-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 2019
AB - We consider the problem of placing arrows, which indicate the direction of each edge in directed graph drawings, without making them overlap other arrows, vertices and edges as much as possible. The following two methods have been proposed for this problem. One is an exact algorithm for the case in which the position of each arrow is restricted to some discrete points. The other is a heuristic algorithm for the case in which the arrow is allowed to move continuously on each edge. In this paper, we assume that the arrow positions are not restricted to discrete points and propose an exact algorithm for the problem of finding an arrow placement such that (a) the weighted sum of the numbers of overlaps with edges, vertices and other arrows is minimized and (b) the sum of the distances between the arrows and their edges' terminal vertices is minimized as a secondary objective. The proposed method solves this problem by reducing it to a mixed integer linear programming problem. Since this is an exponential time algorithm, we add a simple procedure as preprocessing to reduce the running time. Experimental results show that the proposed method can find a better arrow placement than the previous methods and the procedure for reducing the running time is effective.
ER -
English
