!L-Drawings of Directed Graphs

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!L-Drawings of Directed Graphs
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+
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(Γ,
v)
=
KBM
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j)
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AM
(Γ,
j)
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j)
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V
V
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j=1,...,n+1
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)
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i=1,...,n+1 (
)
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+
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(Γ,
v)
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j)
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(Γ,
j)
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(Γ,
j)
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V
V
V
j=1,...,n+1
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8- Ry- R8 p2`iB+2b
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h2bi k, PP.- &_M/QK- AM+`2K2MiH' [email protected]`rBM;b
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AMi2;2` GBM2` S`Q;`K 7Q` JBH/
2
1
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H2M;?i Q7 i?2B` HQM;2bi BM+B/2Mi
b2;K2Mi BM 2+? /B`2+iBQM
3
2
2
2
2
2
1
3
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AMi2;2` GBM2` S`Q;`K 7Q` JBH/
o`B#H2b,
∀i, j = 1, . . . , n,
xij , yij =
*
1 p2`i2t vi HB2b QM +QHmKMf`Qr j
0 Qi?2`rBb2
∀i = 1, . . . , n, Ei , Wi , Ni , Si ≥ 0 7m`i?2bi #2M/ Q7 2/;2b BM+B/2Mi iQ vi
*QMbi`BMib,
+n
+n
∀i = 1, . . . , n, j=1 xij = 1c j=1 yij = 1
+n
+n
∀i, j = 1, . . . , n, xi = j=1 xij · jc yi = j=1 yij · j
QM2 p2`i2t T2` +QHmKMf`Qr
+QQ`/BMi2b Q7 vi
*
#2M/ TH+2K2Mi
∀i = 1, . . . , n, Ei ≥ xi c Wi ≤ xi c Ni ≥ yi c Si ≤ yi
∀(vi , vj ) ∈ G, Ej ≥ xi c Wj ≤ xi c Ni ≥ yj c Si ≤ yj
P#D2+iBp2 6mM+iBQM,
KBM
+n
i=1 (Ni
oBM+2MxQ _Qb2HHB
− Si + Ei − Wi )
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1tT2`BK2MiH MHvbBb
h2bi R, R8 p2`iB+2b- RyW- kyW- jyW- dyW 2/;2b
450
400
350
optimal
incremental
ood
random
Used ink
300
250
200
150
100
50
0
0.1
0.2
0.3
0.7
Edge density
oBM+2MxQ _Qb2HHB
_QK h`2 lMBp2`bBiv
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1tT2`BK2MiH MHvbBb
Saved ink
h2bi k, Ryy- kyy- jyy- 9yy- 8yy p2`iB+2b- jyW 2/;2b
10000
9000
8000
7000
6000
5000
4000
3000
2000
1000
0
incremental
ood
random
100
200
300
400
500
19800 79600 179400 319200 499000
Number of vertices / Theoretical maximum ink
P#b2`piBQM
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