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Diffstat (limited to 'Master/texmf-dist/tex/generic/pgf/graphdrawing/lua/pgf/gd/experimental/evolving/Supergraph.lua')
-rw-r--r-- | Master/texmf-dist/tex/generic/pgf/graphdrawing/lua/pgf/gd/experimental/evolving/Supergraph.lua | 570 |
1 files changed, 570 insertions, 0 deletions
diff --git a/Master/texmf-dist/tex/generic/pgf/graphdrawing/lua/pgf/gd/experimental/evolving/Supergraph.lua b/Master/texmf-dist/tex/generic/pgf/graphdrawing/lua/pgf/gd/experimental/evolving/Supergraph.lua new file mode 100644 index 00000000000..490b8b3191d --- /dev/null +++ b/Master/texmf-dist/tex/generic/pgf/graphdrawing/lua/pgf/gd/experimental/evolving/Supergraph.lua @@ -0,0 +1,570 @@ +-- Copyright 2015 by Malte Skambath +-- +-- This file may be distributed an/or modified +-- +-- 1. under the LaTeX Project Public License and/or +-- 2. under the GNU Public License +-- + +-- Imports +local lib = require "pgf.gd.lib" + +local Vertex = require "pgf.gd.model.Vertex" +local Digraph = require "pgf.gd.model.Digraph" +local Storage = require "pgf.gd.lib.Storage" + + +local declare = require("pgf.gd.interface.InterfaceToAlgorithms").declare + +--- +-- Each |Supergraph| instance is a |Digraph| instance which represents +-- the graph by union operation on all graphs G_i of an evolving graph +-- $G=(G_1, G_2, \dots, G_n)$. Additional to that all references to +-- the snapshot-graphs are shared such that is possible to get access +-- to all vertices for each snapshot graph in a sequence. A vertex of +-- an evolving graph may exists at different times, thus in in +-- different snapshots. Each vertex will be a vertex in the supergraph +-- and if there is a single snapshot in which two vertices are +-- connected by an edge they are connected in the supergraph. +-- +-- Note that in TikZ a \emph{node} is more than a single dot. A node +-- has a content and different properties like background-color or a +-- shape. Formally this can be modelled by function mapping vertices +-- to their properties. For evolving graphs this could be done in the +-- same way. As this is difficult to be realised in PGF because there +-- is no basic support for time dependend properties on nodes, each +-- vertex will be displayed over time by different single +-- (snapshot-)nodes which can have different visual properties. This +-- means for a vertex which we call |supervertex| in the following we +-- will have a (snapshot-)node for each time stamp. +-- +-- \medskip +-- \noindent\emph{Snapshots.} +-- Since an evolving graph is a sequence of different snapshot-graphs +-- $G_i$ each snapshot is assigned to a time +-- +-- +-- @field vertex_snapshots This storage maps each pgf-node to the snapshots +-- in which they are visible. +-- +-- @field supervertices This storage maps each pgf-node to its supervertex +-- which represents all pgf-vertices assigned to the same node +-- +-- @field supervertices_by_id This storage maps a node identifier to the +-- related supervertex such that PGF-nodes which belonging to +-- the same superverticex can be identified +-- +-- @field snapshots An array of all snapshots. Sorted in ascending order +-- over the timestamps of the snapshots. +-- +-- @field arc_snapshots A table storing all snapshots of a supervertex in which +-- the related nodes are connected. Using a snapshot as key you can check +-- if a given snapshot is in the array. +-- +-- Assume we want to iterate over all snapshots +-- for a certain pair of supernodes in which they are connected +-- by an arc. The arc_snapshots storage helps in this case: +-- \begin{codeexample}[code only, tikz syntax=false] +-- local supergraph = Supergraph.generateSupergraph(self.digraph) +-- local u = supergraph.vertices[1] +-- local v = supergraph.vertices[2] +-- +-- local snapshots = supergraph.arc_snapshots[supergraph:arc(u, v)] +-- for _, snapshot in ipairs(snapshots) do +-- do_something(snapshot) +-- end +-- \end{codeexample} +-- +local Supergraph = lib.class { base_class = Digraph } + +-- Namespace +--require("pgf.gd.experimental.evolving").Supergraph = Supergraph + +Supergraph.__index = + function (t, k) + if k == "arcs" then + return Digraph.__index(t,k) + else + return rawget(Supergraph, k) or rawget(Digraph, k) + end + end + +function Supergraph.new(initial) + local supergraph = Digraph.new(initial) + setmetatable(supergraph, Supergraph) + + supergraph.vertex_snapshots = Storage.new() + supergraph.supervertices = Storage.new() + supergraph.supervertices_by_id = {} + supergraph.arc_snapshots = Storage.newTableStorage() + + return supergraph + +end + + +local get_snapshot + +--- +-- Generate or extract a snapshot instance for a given snapshot time. +-- +-- @param snapshots An array of all existing snapshots +-- @param timestamps A table which maps known timestamps to their +-- related snapshots +-- @param ugraph The ugraph of the underlying graph structure +-- @param snapshot_time +-- +-- @return The snapshot instance found in the snapshots array for the +-- wanted timestamp snapshot_time if it does'nt exists a new snapshot +-- will be generated and added to the arrays +-- +function get_snapshot(snapshots, timestamps, ugraph, snapshot_time) + local snapshot + local snapshot_idx = timestamps[snapshot_time] + + if not snapshot_idx then + -- store snapshot if it doesn't exists + snapshot_idx = timestamps.n + 1 + timestamps[snapshot_time] = snapshot_idx + timestamps.n = timestamps.n + 1 + snapshot = Digraph.new { + syntactic_digraph = ugraph.syntactic_digraph, + options = ugraph.options + } + snapshot.timestamp = snapshot_time + snapshots[snapshot_idx] = snapshot + else + snapshot = snapshots[snapshot_idx] + end + assert(snapshot~=nil, "an unexpected error occured") + return snapshot +end + + +--- +-- Generate a new supergraph to describe the whole evolving graph by +-- collecting all temporal information from the digraph and the node +-- options. All nodes in the |digraph| require a |snapshot| and +-- a |supernode| option. To identify a (snapshot-)node with its +-- supernode and snapshot. +-- +-- @param digraph +-- +-- @return The supergraph which is a |Digraph| that has a supervertex +-- for each set of snapshot-vertices with the same |supernode| +-- attribute. +-- +function Supergraph.generateSupergraph(digraph) + local new_supergraph + new_supergraph = Supergraph.new { + syntactic_digraph = digraph.syntactic_digraph, + options = digraph.options, + digraph = digraph, + } + + -- array to store the supervertices for a given vertex name + local local_snapshots = {} -- array to store each snapshot graphs + + local timestamps = { n = 0 } -- set of snapshot times + + -- separate and assign vertices to their snapshots and supervertives + for i,vertex in ipairs(digraph.vertices) do + local snapshot_time = assert(vertex.options["snapshot"], "Missing option 'snapshot' for vertex ".. vertex.name ..". ") + local supernode_name = assert(vertex.options["supernode"], "Missing option 'supernode' for vertex"..vertex.name..". ") + + local snapshot = get_snapshot(local_snapshots, timestamps, digraph, snapshot_time) + local supervertex = new_supergraph.supervertices_by_id[supernode_name] + + if not supervertex then + -- first appeareance of the supernode id + supervertex = Vertex.new { + kind = "super", + name = supernode_name + } + supervertex.snapshots = {} + supervertex.subvertex = {} + new_supergraph.supervertices_by_id[supernode_name] = supervertex + new_supergraph:add{supervertex} + + supervertex.options = {} + supervertex.options = vertex.options + end + + snapshot:add{vertex} + + new_supergraph.supervertices[vertex] = supervertex + new_supergraph.vertex_snapshots[vertex] = snapshot + new_supergraph:addSnapshotVertex(supervertex, snapshot, vertex) + end + + -- Create edges + for i, e in ipairs(digraph.arcs) do + local u,v = e.tail, e.head + local snapshot_tail = new_supergraph.vertex_snapshots[e.tail] + local snapshot_head = new_supergraph.vertex_snapshots[e.head] + + assert(snapshot_head == snapshot_tail, "Arcs must connect nodes that exist at the same time.") + + -- connect in the snapshot graph + local arc = snapshot_tail:connect(u,v) + + -- connect in the supergraph: + local super_tail = new_supergraph.supervertices[u] + local super_head = new_supergraph.supervertices[v] + + new_supergraph:assignToSuperarc(super_tail, super_head, snapshot_tail) + end + + -- snapshots in temporal order + table.sort(local_snapshots, + function(s1,s2) + return s1.timestamp < s2.timestamp + end ) + + local previous_snapshot + + for i,s in ipairs(local_snapshots) do + local start = -math.huge + if previous_snapshot then + start = (s.timestamp - previous_snapshot.timestamp) / 2 + previous_snapshot.timestamp + previous_snapshot.interval.to = start + end + s.interval = { from = start , to = math.huge } + previous_snapshot = s + end + + new_supergraph.snapshots = local_snapshots + new_supergraph.snapshots_indices = Storage.new() + + for i, s in ipairs(new_supergraph.snapshots) do + new_supergraph.snapshots_indices[s] = i + end + + return new_supergraph +end + + +function Supergraph:getSnapshotStaticDuration(snapshot) + assert(snapshot, "a snapshot as parameter expected, but got nil") + local idur = snapshot.interval.to - snapshot.interval.from + assert(idur, "unexpected nil-value") + local d1 = snapshot.interval.to - snapshot.timestamp + local d2 = snapshot.timestamp - snapshot.interval.from + local dm = math.min(d1,d2) + if (idur >= math.huge and dm < math.huge) then + return dm -- [-\infty,t] or [t,\infty] + elseif idur >= math.huge then + return 0 -- only one snapshot [-\infty,\infty] + else + return d1 + d2 -- [t_1, t_2] + end +end + +--- +-- Get the durations of the graph in which snapshots are given which is exactly +-- the time between the first and the last defined snapshot +-- +-- @return The time between the last and first snapshot in seconds +function Supergraph:getDuration() + local first_snapshot = self.snapshots[1] + local last_snapshot = self.snapshots[#self.snapshots] + return last_snapshot.timestamp - first_snapshot.timestamp +end + +--- +-- +-- @return The ratio of the time of a snapshot related to the global duration of the whole +-- evlolving trees. (The time between the last and first snapshot) +function Supergraph:getSnapshotRelativeDuration(snapshot) + if self:getDuration() == 0 then + return 1 + else + return self:getSnapshotStaticDuration(snapshot) / self:getDuration() + end +end + +--- +-- Give the supervertex for a certain pgf-vertex (vertex of a snapshot) +-- +-- @param vertex A vertex of a snapshot. +-- +-- @return A supervertex in the supergraph for the given vertex, nil if no +-- supervertex was assigned before. +-- +function Supergraph:getSupervertex(vertex) + assert(vertex, "vertex required") + assert(self.supervertices, "supervertex table is not defined") + return self.supervertices[vertex] +end + +function Supergraph:getSuperarc(arc) + local superhead = self:getSupervertex(arc.head) + local supertail = self:getSupervertex(arc.tail) + local arc = assert(self:arc(supertail, superhead),"unexpected problem") + return arc +end + +function Supergraph:getSnapshots(supervertex) + return supervertex.snapshots +end + +--- +-- Find the snapshot-instance for a given pgf-vertex +-- (which is a vertex for one certain snapshot) +-- +-- @param vertex A vertex for which you want to get the related snapshot +-- +-- @return The snapshot which contains the given vertex as vertex. +function Supergraph:getSnapshot(vertex) + return self.vertex_snapshots[vertex] +end + +--- +-- For a given supervertex get the related vertex for a snapshot +-- +-- @param supervertex +-- +-- @param snapshot +-- +-- @return The vertex of the supervertex at the specified snapshot +-- +function Supergraph:getSnapshotVertex(supervertex, snapshot) + assert(supervertex, "supervertex must not be nil") + assert(snapshot, "snapshot must not be nil") + return supervertex.subvertex[snapshot] +end + + +function Supergraph:consecutiveSnapshots(snapshot1, snapshot2, n) + assert(snapshot1 and snapshot2, "no snapshot passed") + local idx1 = self.snapshots_indices[snapshot1] --or -1 + local idx2 = self.snapshots_indices[snapshot2] --or -1 + local d = n or 1 + + return (idx2-idx1 <= d) or (idx1-idx2 <= d) +end + +function Supergraph:consecutive(vertex1, vertex2, n) + local s1 = self:getSnapshot(vertex1) + local s2 = self:getSnapshot(vertex2) + return self:consecutiveSnapshots(s1, s2, n) +end + +--- +-- Write pack all position information to the nodes of each snapshot +-- such that all nodes with the same supervertex have the same position +-- +-- @param ugraph An undirected graph for which the vertices should get +-- their positions from the supergraph. +-- +function Supergraph:sharePositions(ugraph, ignore) + + for _,vertex in ipairs(ugraph.vertices) do + if not ignore then + vertex.pos.x = self.supervertices[vertex].pos.x + vertex.pos.y = self.supervertices[vertex].pos.y + else + if not ignore.x then + vertex.pos.x = self.supervertices[vertex].pos.x + end + if not ignore.y then + vertex.pos.y = self.supervertices[vertex].pos.y + end + end + + + end +end + +function Supergraph:onAllSnapshotvertices(f, ugraph) + for _,vertex in ipairs(ugraph.vertices) do + local snapshot_vertex = self.supertvertices[vertex] + if snapshot_vertex then + f(vertex, snapshot_vertex) + end + end +end + +--- +-- Split a supervertex into new supervertices such that +-- for a given snapshot there is a new pseudo-supervertex. +-- This pseudo-supervertex will be assigned to all snapshots +-- after the given snapshot. +-- All snapshots of a new pseudo-supervertex are removed from +-- the original vertex. +-- If a supervertex has no subvertices then it will not be added to the graph. +-- +-- @param supervertex The supervertex which should be splitted. +-- +-- @param snapshots An array of snapshots at which the supervertex +-- should be splitted into a new one with the corresponding pgf-vertices. +-- If there are more than one snapshots passed to the function +-- for each snapshot there will be a new pseudo-vertex +-- +function Supergraph:splitSupervertex(supervertex, snapshots) + assert(supervertex, "no supervertex defined") + -- snapshots in temporal order + table.sort(snapshots, + function(s1,s2) + return s1.timestamp < s2.timestamp + end ) + + assert(#snapshots~=0) + + local edit_snapshots = supervertex.snapshots + local first_removed = math.huge + local rem_arcs = {} + for i = 1, #snapshots do + local s_first = self.snapshots_indices[snapshots[i]] + first_removed = math.min(s_first,first_removed) + local s_last + if i==#snapshots then + s_last = #self.snapshots + else + s_last = self.snapshots_indices[snapshots[i+1]]-1 + end + + local pseudovertex = Vertex.new { + kind = "super", + name = supervertex.name.."*"..i, + subvertex = {}, + snapshots = {} + } + + local has_subvertices = false + + for j = s_first, s_last do + local s = self.snapshots[j] + local vertex = self:getSnapshotVertex(supervertex, s) + if vertex then + self.supervertices[vertex] = pseudovertex + self:addSnapshotVertex(pseudovertex, s, vertex) + self:removeSnapshotVertex(supervertex, s) + + if not has_subvertices then + has_subvertices = true + self:add{pseudovertex} + end + + -- update edges: + local incoming = self.digraph:incoming(vertex) + local outgoing = self.digraph:outgoing(vertex) + + for _, arc in ipairs(incoming) do + local tail = self.supervertices[arc.tail] + local head = self.supervertices[arc.head] + self:assignToSuperarc(tail, pseudovertex, s) + + local super_arc = self:arc(tail, supervertex) + if not rem_arcs[super_arc] then + table.insert(rem_arcs, {arc = super_arc, snapshot = s}) + rem_arcs[super_arc] = true + end + end + + for _, arc in ipairs(outgoing) do + local tail = self.supervertices[arc.tail] + local head = self.supervertices[arc.head] + self:assignToSuperarc(pseudovertex, head, s) + + local super_arc = self:arc(supervertex, head) + if not rem_arcs[super_arc] then + table.insert(rem_arcs, {arc = super_arc, snapshot = s}) + rem_arcs[super_arc] = true + end + end + end + end + end + + if first_removed ~= math.huge then + for _, removed_arc in ipairs(rem_arcs) do + local snapshots = self.arc_snapshots[removed_arc.arc] + for i=#snapshots,1,-1 do + local s = snapshots[i] + if s.timestamp >= removed_arc.snapshot.timestamp then + table.remove(snapshots, i) + end + end + + if #snapshots==0 then + self:disconnect(removed_arc.arc.tail, removed_arc.arc.head) + end + end + end +end + +-- function Supergraph:reloadArcSnapshots() +-- for _, arc in ipairs(self.digraph.arcs) do +-- local snapshot = self:getSnapshot(arc.head) +-- local superarc = self:getSuperarc(arc) +-- texio.write("\n"..arc.tail.name..">"..arc.head.name) +-- self.arc_snapshots[superarc] = snapshot +-- end +-- end + +--- +-- Remove the binding of a vertex at a certain snapshot from its assigned +-- supervertex. +-- This requires time $O(n)$ where $n$ is the number of nodes actually +-- assigned to the supervertex. +function Supergraph:removeSnapshotVertex(supervertex, snapshot) + assert(supervertex and snapshot,"missing argument: the supervertex and snapshot must not be nil") + + -- remove reference to snapshot + for i = #supervertex.snapshots,1,-1 do + if supervertex.snapshots[i] == snapshot then + table.remove(supervertex.snapshots, i) + end + end + -- remove vertex at snapshot + supervertex.subvertex[snapshot] = nil +end + +--- +-- Assign a vertex to a snapshot vertex of this supergraph. +-- This requires time $O(1)$ +-- @param supervertex +-- +-- @param snapshot +-- +-- @param vertex The vertex which should be assigned to the supervertex +-- for the given snapshot. +-- +function Supergraph:addSnapshotVertex(supervertex, snapshot, vertex) + supervertex.subvertex[snapshot] = vertex + table.insert(supervertex.snapshots, snapshot) +end + +--- +-- Assign a given snapshot to the superarc between two supernodes. +-- If still no arc between those nodes exists a new edges will +-- be created. +-- This requires time $O(n)$ where $n$ is the number of snapshots already +-- assigned to the given arc. +-- +-- @param super_tail The tail of the directed arc in the supergraph. +-- +-- @param super_head The head of the directed arc in the supergraph. +-- +-- @param snapshot A snapshot in which both nodes are connected. +-- +-- @return The arc which was created or updated. +-- +function Supergraph:assignToSuperarc(super_tail, super_head, snapshot) + assert(self:contains(super_tail) and self:contains(super_head), + "tried to connect supernodes not in the supergraph") + + local super_arc = self:arc(super_tail, super_head) + if not super_arc then + super_arc = self:connect(super_tail, super_head) + end + + table.insert(self.arc_snapshots[super_arc], snapshot) + self.arc_snapshots[super_arc][snapshot] = true + + return super_arc +end + +return Supergraph + |