Changes for page The Five Phases

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8	8
9	9	The reversed edges have to be restored at some point. There's a processor for that, called ReversedEdgeRestorer. All implementations of phase one must include a dependency on that processor, to be included after phase 5.
10	10
11		-=== Precondition ===
12		-
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	12	+Preconditions
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13	13	* No node is assigned to a layer yet.
14		-
15		-=== Postcondition ===
16		-
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17	17	* The graph is now cycle-free. Still, no node is assigned to a layer yet.
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	25	+Remarks
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	27	+* All implementations of phase one must include a dependency on the {{code language="none"}}ReversedEdgeRestorer{{/code}}, to be included after phase five.
	28	+)))
	29	+|(% class="highlight" %)(% class="highlight" %)
	30	+(((
	31	+Implementations
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	33	+* {{code language="none"}}GreedyCycleBreaker{{/code}}. Uses a greedy approach to cycle-breaking.
	34	+)))
18	18
19		-=== Remarks ===
20		-
21		-* All implementations of phase one must include a dependency on the ReversedEdgeRestorer, to be included after phase 5.
22		-
23		-=== Current Implementations ===
24		-
25		-* GreedyCycleBreaker. Uses a greedy approach to cycle-breaking.
26		-
27	27	== Phase 2: Layering ==
28	28
29	29	The second phase assigns nodes to layers. (also called //ranks// in some papers) Nodes in the same layer are assigned the same x coordinate. (give or take) The problem to solve here is to assign each node x a layer i such that each successor of x is in a layer j>i. The only exception are self-loops, that may or may not be supported by later phases.
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32	32
33	33	Note that nodes can have a property associated with them that constraints the layers they can be placed in.
34	34
35		-=== Precondition ===
36		-
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37	37	* The graph is cycle-free.
38	38	* The nodes have not been layered yet.
39		-
40		-=== Postcondition ===
41		-
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42	42	* The graph has a layering.
	56	+)))
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	59	+Remarks
	60	+)))|(((
	61	+* Implementations should usually include a dependency on the {{code language="none"}}LayerConstraintHandler{{/code}}, unless they already adhere to layer constraints themselves.
	62	+)))
	63	+|(% class="highlight" %)(% class="highlight" %)
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	65	+Implementations
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	67	+* {{code language="none"}}LongestPathLayerer{{/code}}. Layers nodes according to the longest paths between them. Very simple, and doesn't usually give the best results.
	68	+* {{code language="none"}}NetworkSimplexLayerer{{/code}}. A way more sophisticated algorithm whose results are usually very good.
	69	+)))
43	43
44		-=== Remarks ===
45		-
46		-* Implementations should usually include a dependency on the LayerConstraintHandler, unless they already adhere to layer constraints themselves.
47		-
48		-=== Current Implementations ===
49		-
50		-* LongestPathLayerer. Layers nodes according to the longest paths between them. Very simple, but doesn't usually give the best results.
51		-* NetworkSimplexLayerer. A way more sophisticated algorithm whose results are usually very good.
52		-
53	53	== Phase 3: Crossing Reduction ==
54	54
55		-The objective of phase 3 is to determine how the nodes in each layer should be ordered. The order determines the number of edge crossings, and thus is a critical step towards readable diagrams. Unfortunately, the problem is NP-hard even for only two layers. Did I just hear you saying "heuristic"? The usual approach is to sweep through the pairs of layers from left to right and back, along the way applying some heuristic to minimize crossings between each pair of layers. The two most prominent and well-studied kinds of heuristics used here are the barycenter method and the median method. We have currently implemented the former.
	73	+The objective of phase 3 is to determine how the nodes in each layer should be ordered. The order determines the number of edge crossings, and thus is a critical step towards readable diagrams. Unfortunately, the problem is NP-hard even for only two layers. Did I just hear you say "heuristic"? The usual approach is to sweep through the pairs of layers from left to right and back, along the way applying some heuristic to minimize crossings between each pair of layers. The two most prominent and well-studied kinds of heuristics used here are the barycenter method and the median method. We have currently implemented the former.
56	56
57	57	Our crossing reduction implementations may or may not support the concepts of node successor constraints and layout groups. The former allows a node x to specify a node y!=x that may only appear after x. Layout groups are groups of nodes. Nodes belonging to different layout groups are not to be interleaved.
58	58
59		-=== Precondition ===
60		-
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61	61	* The graph has a proper layering. (except for self-loops)
62	62	* An implementation may allow in-layer connections.
63		-* Usually, all Nodes are required to have at least fixed port sides.
64		-
65		-=== Postcondition ===
66		-
	83	+* Usually, all nodes are required to have a least fixed port sides.
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	87	+Postconditions
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67	67	* The order of nodes in each layer is fixed.
68	68	* All nodes have a fixed port order.
69		-
70		-=== Remarks ===
71		-
72		-* If fixed port sides are required, the PortPositionProcessor may be of use.
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	94	+Remarks
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	96	+* If fixed port sides are required, the {{code language="none"}}PortPositionProcessor{{/code}} may be of use.
73	73	* Support for in-layer connections may be required to be able to handle certain problems. (odd port sides, for instance)
	98	+)))
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	101	+Implementations
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	103	+* {{code language="none"}}LayerSweepCrossingMinmizer{{/code}}. Does several sweeps across the layers, minimizing the crossings between each pair of layers using a barycenter heuristic. Supports node successor constraints and layout groups. Node successor constraints require one node to appear before another node. Layout groups specify sets of nodes whose nodes must not be interleaved.
	104	+)))
74	74
75		-=== Current Implementations ===
76		-
77		-* [[LayerSweepCrossingMinimizer>>doc:Layer Sweep Crossing Minimization]]. Does several sweeps across the layers, minimizing the crossings between each pair of layers using a barycenter heuristic. Supports node successor constraints and layout groups. Node successor constraints require one node to appear before another node. Layout groups specify sets of nodes whose nodes must not be interleaved.
78		-
79	79	== Phase 4: Node Placement ==
80	80
81	81	So far, the coordinates of the nodes have not been touched. That's about to change in phase 4, which determines the y coordinate. While phase 3 has an impact on the number of edge crossings, phase 4 has an influence on the number of edge bends. Usually, some kind of heuristic is employed to yield a good y coordinate.
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82	82
83	83	Our node placers may or may not support node margins. Node margins define the space occupied by ports, labels and such. The idea is to keep that space free from edges and other nodes.
84	84
85		-=== Precondition ===
86		-
	112	+|=(((
	113	+Preconditions
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87	87	* The graph has a proper layering. (except for self-loops)
88	88	* Node orders are fixed.
89	89	* Port positions are fixed.
90	90	* An implementation may allow in-layer connections.
91	91	* An implementation may require node margins to be set.
92		-
93		-=== Postcondition ===
94		-
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	124	+Postconditions
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95	95	* Each node is assigned a y coordinate such that no two nodes overlap.
96	96	* The height of each layer is set.
97	97	* The height of the graph is set to the maximal layer height.
98		-
99		-=== Remarks ===
100		-
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101	101	* Support for in-layer connections may be required to be able to handle certain problems. (odd port sides, for instance)
102		-* If node margins are supported, the NodeMarginCalculator can compute them.
103		-* Port positions can be fixed by using the PortPositionProcessor.
	135	+* If node margins are supported, the {{code language="none"}}NodeMarginCalculator{{/code}} can compute them.
	136	+* Port positions can be fixed by using the {{code language="none"}}PortPositionProcessor{{/code}}.
	137	+)))
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	140	+Implementations
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	142	+
104	104
105		-=== Current Implementations ===
	144	+{{code language="none"}}
	145	+LinearSegmentsNodePlacer
	146	+{{/code}}
106	106
107		-* LinearSegmentsNodePlacer. Builds linear segments of nodes that should have the same y coordinate and tries to respect those linear segments. Linear segments are placed according to a barycenter heuristic.
	148	+. Builds linear segments of nodes that should have the same y coordinate and tries to respect those linear segments. Linear segments are placed according to a barycenter heuristic.
	149	+)))
108	108
109	109	== Phase 5: Edge Routing ==
110	110
111	111	In the last phase, it's time to determine x coordinates for all nodes and route the edges. The routing may support very different kinds of features, such as support for odd port sides, (input ports that are on the node's right side) orthogonal edges, spline edges etc. Often times, the set of features supported by an edge router largely determines the intermediate processors used during the layout process.
112	112
113		-=== Precondition ===
114		-
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115	115	* The graph has a proper layering. (except for self-loops)
116	116	* Nodes are assigned y coordinates.
117	117	* Layer heights are correctly set.
118	118	* An implementation may allow in-layer connections.
119		-
120		-=== Postcondition ===
121		-
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	166	+Postconditions
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122	122	* Nodes are assigned x coordinates.
123	123	* Layer widths are set.
124	124	* The graph's width is set.
125	125	* The bend points of all edges are set.
126		-
127		-=== Remarks ===
128		-
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	175	+Remarks
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129	129	None.
130		-
131		-=== Current Implementations ===
132		-
133		-* ComplexSplineRouter. TODO: Document.
134		-* OrthogonalEdgeRouter. Routes edges orthogonally. Supports routing edges going into an eastern port around a node. Tries to minimize the width of the space between each pair of layers used for edge routing.
135		-* PolylineEdgeRouter. TODO: Document.
136		-* SimpleSplineEdgeRouter. TODO: Document.
	178	+)))
	179	+|(% class="highlight" %)(% class="highlight" %)
	180	+(((
	181	+Implementations
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	183	+* {{code language="none"}}ComplexSplineRouter{{/code}}.
	184	+* {{code language="none"}}OrthogonalEdgeRouter{{/code}}. Routes edges orthogonally. Supports routing edges going into an eastern port around a node. Tries to minimize the width of the space between each pair of layers used for edge routing.
	185	+* {{code language="none"}}PolylineEdgeRouter{{/code}}.
	186	+* {{code language="none"}}impleSplineEdgeRouter{{/code}}.
	187	+)))

Confluence.Code.ConfluencePageClass[0]

Id

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1		-884898
	1	+884909

URL

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1		-https://rtsys.informatik.uni-kiel.de/confluence//wiki/spaces/KIELER/pages/884898/The Five Phases
	1	+https://rtsys.informatik.uni-kiel.de/confluence//wiki/spaces/KIELER/pages/884909/The Five Phases