E. DI GIACOMO, G. LIOTTA, AND S. WISMATH, Drawing series-parallel graphs on a box. In Proc. 14th Canadian Conf. on Computational Geometry (CCCG '02), pp. 149--153, The University of Lethbridge, Canada, 2002.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....Z. That is, the volume of a polyline drawing is the number of gridpoints in the bounding box. This definition is formulated so that two dimensional drawings have positive volume. We are interested in polyline drawings with small volume. The volume of straight line drawings has been widely studied [21, 26, 31, 37, 41, 42, 51, 103, 107, 125]. Three dimensional graph drawings in which the vertices are allowed real coordinates have also been studied [23, 28, 29, 34, 43, 59, 78 81, 93, 102] Aesthetic criteria besides volume that have been considered include symmetry [78 81] aspect ratio [29, 59] angular resolution [29, 59] ....

E. DI GIACOMO, G. LIOTTA, AND S. WISMATH, Drawing series-parallel graphs on a box. In S. WISMATH, ed., Proc. 14th Canadian Conf. on Computational Geometry (CCCG '02), pp. 149--153, The University of Lethbridge, Canada, 2002.

....Z drawing with volume X Z. That is, the volume of a 3D drawing is the number of gridpoints in the bounding box. This definition is formulated so that 2D drawings have positive volume. We are interested in 3D drawings with small volume. The volume of 3D drawings has been widely studied [3, 6, 9, 11, 14, 16, 19, 36 38, 40]. Three dimensional graph drawings in which the vertices are allowed real coordinates have also been studied [5, 7, 8, 10, 17, 21, 26 29, 32, 35] Aesthetic criteria besides volume which have been considered include symmetry [26 29] aspect # Research supported by NSERC and FCAR. Completed ....

E. DI GIACOMO, G. LIOTTA, AND S. WISMATH, Drawing series-parallel graphs on a box. In S. W ISMATH, ed., Proc. 14th Canadian Conf. on Computational Geometry (CCCG '02), pp. 149--153, The University of Lethbridge, Canada, 2002.

....grid drawings with linear volume, which is the largest known class of graphs admitting such drawings. Motivated by applications in information visualisation, VLSI layout, and software engineering (see [12] there is a growing body of research in three dimensional straight line graph drawing [4, 6, 8, 12, 13, 24, 26, 35]. The remainder of the paper is organised as follows. Section 1.1 recalls a number of definitions and well known results. In Sections 1.2, 1.3 and 1.4 we survey and state our results for tree partitions, queue layouts and threedimensional graph drawings, respectively. In Section 2 we prove the ....

....a three dimensional drawing is contained in an axis aligned box with side lengths X 1, Y 1 and Z 1, then we speak of a X Y Z drawing with volume X Y Z. We are interested in three dimensional drawings with small volume. The volume of three dimensional drawings has been extensively studied [4, 6, 8, 12, 13, 24, 26, 35]. Cohen, Eades, Lin, and Ruskey [6] proved that every graph has a three dimensional drawing with O(n ) volume, and this bound is asymptotically tight for the complete graph Kn . It is therefore of interest to identify fixed graph parameters which allow for three dimensional drawings with O(n ....

[Article contains additional citation context not shown here]

E. DI GIACOMO, G. LIOTTA, AND S. WISMATH, Drawing series-parallel graphs on a box. In S. WISMATH, ed., Proc. 14th Canadian Conf. on Computational Geometry (CCCG '02), The University of Lethbridge, Canada, 2002.

....drawing around a triangular prism; see Lemma 5 for more on this method. Poranen [32] proved that seriesparallel digraphs have upward three dimensional drawings with O(n ) volume, and that this bound can be improved to O(n ) and O(n) in certain special cases. Recently di Giacomo et al. [11] proved that series parallel graphs with maximum degree three have three dimensional drawings with linear volume. Note that three dimensional drawings with the vertices having real coordinates have been studied by Bru and Frick [4] Chilakamarri et al. 6] Chrobak et al. 7] Cruz and Twarog ....

E. DI GIACOMO, G. LIOTTA, AND S. WISMATH, Drawing series-parallel graphs on a box. In S. WISMATH, ed., Proc. 14th Canadian Conf. on Computational Geometry (CCCG '02), The University of Lethbridge, Canada, 2002.

....who proved that every outerplanar graph has a drawing with O(n) volume. Poranen [25] proved that series parallel digraphs have upward three dimensional drawings with O(n ) volume, and that this bound can be improved to O(n ) and O(n) in certain special cases. di Giacomo, Liotta, and Wismath [7] proved that series parallel graphs with maximum degree three have three dimensional drawings with O(n) volume. Dujmovic, Morin, and Wood [12] proved that every graph G has a three dimensional drawing with O(n pw(G) volume. This implies O(n log n) volume drawings for graphs of bounded ....

....tree width at most two (series parallel graphs) and (4) graphs of bounded tree width and bounded maximum degree. Corollary 1 improves and or generalises the above mentioned results for three dimensional drawings of outerplanar graphs, series parallel graphs, and graphs of bounded tree width in [7, 12, 14, 25]. Note that the algorithm by Felsner et al. 14] closely parallels the construction of 2 queue layouts of outerplanar graphs due to Rengarajan and Veni Madhavan [26] both of which are based on breadth first search, as is one of our proofs to follows. 3 Queue Layouts and Tree Width In this ....

E. DI GIACOMO, G. LIOTTA, AND S. WISMATH, Drawing series-parallel graphs on a box. In S. WISMATH, ed., Proc. 14th Canadian Conf. on Computational Geometry (CCCG '02), The University of Lethbridge, Canada, 2002.

....who proved that every outerplanar graph has a drawing with O(n) volume. Poranen [21] proved that series parallel digraphs have upward threedimensional drawings with O(n ) volume, and that this bound can be improved to O(n ) and O(n) in certain special cases. di Giacomo, Liotta, and Wismath [6] proved that series parallel graphs with maximum degree three have three dimensional drawings with O(n) volume. Dujmovic, Morin, and Wood [10] proved that every graph G has a three dimensional drawing with ) volume. This implies O(n log n) volume drawings for graphs of bounded treewidth, such ....

....of treewidth at most two (series parallel graphs) and (4) graphs of bounded treewidth and bounded maximum degree. Corollary 1 improves and or generalises the above mentioned results for three dimensional drawings of outerplanar graphs, series parallel graphs, and graphs of bounded treewidth in [6, 10, 11, 21]. Note that the algorithm by Felsner et al. 11] closely parallels the construction of 2 queue layouts of outerplanar graphs due to Rengarajan and Veni Madhavan [22] both of which are based on breadth first search, as is one of our proofs to follows. 3 Queue Layouts and Treewidth In this ....

E. DI GIACOMO, G. LIOTTA, AND S. WISMATH, Drawing series-parallel graphs on a box. In S. WISMATH, ed., Proc. 14th Canadian Conf. on Computational Geometry (CCCG '02), The University of Lethbridge, Canada, to appear.

No context found.

E. Di Giacomo, G. Liotta and S.K. Wismath. Drawing Series-Parallel Graphs on a Box. 14th Canadian Conference On Computational Geometry (CCCG '02), pages 149--153, 2002.

....all 4 tracks and the 6 line segments between them, thus blocking any edges from passing through it. Then 3 copies of it are arranged as in Figure 13. It can even be shown that there are series parallel graphs that are not boxdrawable, but almost all series parallel graphs are drawable on 8 lines [11]. 3.3 Other Directions There are several directions being considered to solve the 3D case for planar graphs. Can all planar graphs be drawn on these grids: 2 k n k n n (this has a constant aspect ratio) Complexity Issues: Given a graph G and a grid , can G be drawn on ....

E. di Giacomo, G. Liotta, and S. Wismath. Drawing series-parallel graphs on a box. In S. Wismath, editor, Proc. 14th Canadian Conf. on Computational Geometry (CCCG '02), Canada, 2002. The University of Lethbridge.

....result by Dujmovic and Wood [17] shows that linear volume can also be achieved for graphs with bounded treewidth; they show 3D straight line grid drawings of volume c n for these graphs, where c is a constant whose value exponentially depends on the tree width. Di Giacomo, Liotta, and Wismath [16] show 4 n volume for a subclass of seriesparallel graphs. The problem of computing straight line 3D drawings of planar graphs on an integer grid of o(n ) volume is still open. A recent lower bound on the volume of 3D straight line drawings as a function of the number of edges is obtained by ....

E. Di Giacomo, G. Liotta and S.K. Wismath. Drawing Series-Parallel Graphs on a Box. 14th Canadian Conference On Computational Geometry (CCCG '02), pages 149-153, 2002.

No context found.

E. DI GIACOMO, G. LIOTTA, AND S. WISMATH, Drawing series-parallel graphs on a box. In Proc. 14th Canadian Conf. on Computational Geometry (CCCG '02), pp. 149--153, The University of Lethbridge, Canada, 2002.

No context found.

E. DI GIACOMO, G. LIOTTA, AND S. WISMATH, Drawing series-parallel graphs on a box. In Proc. 14th Canadian Conf. on Computational Geometry (CCCG '02), pp. 149--153, The University of Lethbridge, Canada, 2002.

No context found.

E. Di Giacomo, G. Liotta, and S. Wismath, Drawing series-parallel graphs on a box, in Proc. 14th Canadian Conf. on Computational Geometry (CCCG '02), The University of Lethbridge, Canada, 2002, pp. 149-153.

No context found.

E. DI GIACOMO, G. LIOTTA, AND S. WISMATH, Drawing series-parallel graphs on a box. In Proc. 14th Canadian Conf. on Computational Geometry (CCCG '02), pp. 149--153, The University of Lethbridge, Canada, 2002.

No context found.

Emilio Di Giacomo, Giuseppe Liotta, and Stephen Wismath, Drawing series-parallel graphs on a box, 14th Canadian Conf. on Computational Geometry (CCCG '02), The University of Lethbridge, Canada, 2002, pp. 149-153.

No context found.

E. DI GIACOMO, G. LIOTTA, AND S. WISMATH, Drawing series-parallel graphs on a box. In Proc. 14th Canadian Conf. on Computational Geometry (CCCG '02), pp. 149--153, The University of Lethbridge, Canada, 2002.

No context found.

E. di Giacomo, G. Liotta, and S. Wismath, Drawing series-parallel graphs on a box. In S. Wismath, ed., Proc. 14th Canadian Conf. on Computational Geometry (CCCG '02), The University of Lethbridge, Canada, 2002.

No context found.

E. DI GIACOMO, G. LIOTTA, AND S. WISMATH, Drawing series-parallel graphs on a box. In S. WISMATH, ed., Proc. 14th Canadian Conf. on Computational Geometry (CCCG '02), The University of Lethbridge, Canada, 2002.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC