--- /dev/null
+# Graph topology utilities, used by KCC
+#
+# Copyright (C) Andrew Bartlett 2015
+#
+# Copyright goes to Andrew Bartlett, but the actual work was performed
+# by Douglas Bagnall and Garming Sam.
+#
+# This program is free software; you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation; either version 3 of the License, or
+# (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program. If not, see <http://www.gnu.org/licenses/>.
+
+import sys
+import itertools
+
+
+def write_dot_file(basename, edge_list, vertices=None, label=None, destdir=None,
+ reformat_labels=True, directed=False, debug=None):
+ from tempfile import NamedTemporaryFile
+ if label:
+ basename += '_' + label.translate(None, ', ') #fix DN, guid labels
+ f = NamedTemporaryFile(suffix='.dot', prefix=basename + '_', delete=False, dir=destdir)
+ if debug is not None:
+ debug(f.name)
+ graphname = ''.join(x for x in basename if x.isalnum())
+ print >>f, '%s %s {' % ('digraph' if directed else 'graph', graphname)
+ print >>f, 'label="%s";\nfontsize=20;' % (label or graphname)
+ if vertices:
+ for v in vertices:
+ if reformat_labels:
+ v = v.replace(',', '\\n')
+ print >>f, '"%s";' % (v,)
+ for a, b in edge_list:
+ if reformat_labels:
+ a = a.replace(',', '\\n')
+ b = b.replace(',', '\\n')
+ line = '->' if directed else '--'
+ print >>f, '"%s" %s "%s";' % (a, line, b)
+ print >>f, '}'
+ f.close()
+
+
+
+class KCCGraphError(Exception):
+ pass
+
+def verify_graph_complete(edges, vertices, edge_vertices):
+ """The graph is complete, which is to say there is an edge between
+ every pair of nodes."""
+ for v in vertices:
+ remotes = set()
+ for a, b in edges:
+ if a == v:
+ remotes.add(b)
+ elif b == v:
+ remotes.add(a)
+ if len(remotes) + 1 != len(vertices):
+ raise KCCGraphError("graph is not fully connected")
+
+
+def verify_graph_connected(edges, vertices, edge_vertices):
+ """There is a path between any two nodes."""
+ if not edges:
+ if len(vertices) <= 1:
+ return
+ raise KCCGraphError("disconnected vertices were found:\nvertices: %s\n edges: %s" %
+ (sorted(vertices), sorted(edges)))
+
+ remaining_edges = list(edges)
+ reached = set(remaining_edges.pop())
+ while True:
+ doomed = []
+ for i, e in enumerate(remaining_edges):
+ a, b = e
+ if a in reached:
+ reached.add(b)
+ doomed.append(i)
+ elif b in reached:
+ reached.add(a)
+ doomed.append(i)
+ if not doomed:
+ break
+ for i in reversed(doomed):
+ del remaining_edges[i]
+
+ if remaining_edges or reached != vertices:
+ raise KCCGraphError("graph is not connected:\nvertices: %s\n edges: %s" %
+ (sorted(vertices), sorted(edges)))
+
+
+
+def verify_graph_forest(edges, vertices, edge_vertices):
+ """The graph contains no loops. A forest that is also connected is a
+ tree."""
+ trees = [set(e) for e in edges]
+ while True:
+ for a, b in itertools.combinations(trees, 2):
+ intersection = a & b
+ if intersection:
+ if len(intersection) == 1:
+ a |= b
+ trees.remove(b)
+ break
+ else:
+ raise KCCGraphError("there is a loop in the graph")
+ else:
+ # no break in itertools.combinations loop means no
+ # further mergers, so we're done.
+ #
+ # XXX here we also know whether it is a tree or a
+ # forest by len(trees) but the connected test already
+ # tells us that.
+ return
+
+def verify_graph_multi_edge_forest(edges, vertices, edge_vertices):
+ """This allows a forest with duplicate edges. That is if multiple
+ edges go between the same two vertices, they are treated as a
+ single edge by this test.
+
+ e.g.:
+ o
+ pass: o-o=o o=o (|) fail: o-o
+ `o o `o'
+ """
+ unique_edges = set(edges)
+ trees = [set(e) for e in unique_edges]
+ while True:
+ for a, b in itertools.combinations(trees, 2):
+ intersection = a & b
+ if intersection:
+ if len(intersection) == 1:
+ a |= b
+ trees.remove(b)
+ break
+ else:
+ raise KCCGraphError("there is a loop in the graph")
+ else:
+ return
+
+
+def verify_graph_forest_of_rings(edges, vertices, edge_vertices):
+ """The graph should consist of clusters of node connected in rings,
+ with the connections between the cdlusters forming a forest."""
+ pass
+
+
+def verify_graph_no_lonely_vertices(edges, vertices, edge_vertices):
+ """There are no vertices without edges."""
+ lonely = vertices - edge_vertices
+ if lonely:
+ raise KCCGraphError("some vertices are not connected:\n%s" % '\n'.join(sorted(lonely)))
+
+
+def verify_graph_no_unknown_vertices(edges, vertices, edge_vertices):
+ """The edge endpoints contain no vertices that are otherwise unknown."""
+ unknown = edge_vertices - vertices
+ if unknown:
+ raise KCCGraphError("some edge vertices are seemingly unknown:\n%s" % '\n'.join(sorted(unknown)))
+
+
+def verify_graph_directed_double_ring(edges, vertices, edge_vertices):
+ """Each node has at least two directed edges leaving it, and two
+ arriving. The edges work in pairs that have the same end points
+ but point in opposite directions. The pairs form a path that
+ touches every vertex and form a loop.
+
+ There might be other connections that *aren't* part of the ring.
+ """
+ #XXX possibly the 1 and 2 vertex cases are special cases.
+ if not edges:
+ return
+ if len(edges) < 2* len(vertices):
+ raise KCCGraphError("directed double ring requires at least twice as many edges as vertices")
+
+ exits = {}
+ for start, end in edges:
+ s = exits.setdefault(start, [])
+ s.append(end)
+
+ try:
+ #follow both paths at once -- they should be the same length
+ #XXX there is probably a simpler way.
+ forwards, backwards = exits[start]
+ fprev, bprev = (start, start)
+ f_path = [start]
+ b_path = [start]
+ for i in range(len(vertices)):
+ a, b = exits[forwards]
+ if a == fprev:
+ fnext = b
+ else:
+ fnext = a
+ f_path.append(forwards)
+ fprev = forwards
+ forwards = fnext
+
+ a, b = exits[backwards]
+ if a == bprev:
+ bnext = b
+ else:
+ bnext = a
+ b_path.append(backwards)
+ bprev = backwards
+ backwards = bnext
+
+ except ValueError, e:
+ raise KCCGraphError("wrong number of exits '%s'" % e)
+
+ f_set = set(f_path)
+ b_set = set(b_path)
+
+ if (f_path != list(reversed(b_path)) or
+ len(f_path) != len(f_set) + 1 or
+ len(f_set) != len(vertices)):
+ raise KCCGraphError("doesn't seem like a double ring to me!")
+
+
+def verify_graph_directed_double_ring_or_small(edges, vertices, edge_vertices):
+ if len(vertices) < 3:
+ return
+ return verify_graph_directed_double_ring(edges, vertices, edge_vertices)
+
+
+
+def verify_graph(title, edges, vertices=None, directed=False, properties=(), fatal=True,
+ debug=None):
+ errors = []
+ if debug is None:
+ def debug(*args): pass
+
+ debug("%sStarting verify_graph for %s%s%s" % (PURPLE, MAGENTA, title, C_NORMAL))
+
+ properties = [x.replace(' ', '_') for x in properties]
+
+ edge_vertices = set()
+ for a, b in edges:
+ edge_vertices.add(a)
+ edge_vertices.add(b)
+
+ if vertices is None:
+ vertices = edge_vertices
+ else:
+ vertices = set(vertices)
+ if vertices != edge_vertices:
+ debug("vertices in edges don't match given vertices:\n %s != %s" %
+ (sorted(edge_vertices), sorted(vertices)))
+
+ for p in properties:
+ fn = 'verify_graph_%s' % p
+ try:
+ f = globals()[fn]
+ except KeyError:
+ errors.append((p, "There is no verification check for '%s'" % p))
+ try:
+ f(edges, vertices, edge_vertices)
+ debug(" %s%18s:%s verified!" % (DARK_GREEN, p, C_NORMAL))
+ except KCCGraphError, e:
+ errors.append((p, e))
+
+ if errors:
+ if fatal:
+ raise KCCGraphError("The '%s' graph lacks the following properties:\n%s" %
+ (title, '\n'.join('%s: %s' % x for x in errors)))
+ debug(("%s%s%s FAILED:" % (MAGENTA, title, RED)))
+ for p, e in errors:
+ debug(" %18s: %s%s%s" %(p, DARK_YELLOW, e, RED))
+ debug(C_NORMAL)
+
+
+
+def verify_and_dot(basename, edges, vertices=None, label=None, destdir=None,
+ reformat_labels=True, directed=False, properties=(), fatal=True,
+ debug=None, verify=True, dot_files=False):
+
+ title = '%s %s' % (basename, label or '')
+ if verify:
+ verify_graph(title, edges, vertices, properties=properties, fatal=fatal,
+ debug=debug)
+ if dot_files:
+ write_dot_file(basename, edges, vertices=vertices, label=label, destdir=destdir,
+ reformat_labels=reformat_labels, directed=directed, debug=debug)
+
+def list_verify_tests():
+ for k, v in sorted(globals().items()):
+ if k.startswith('verify_graph_'):
+ print k.replace('verify_graph_', '')
+ if v.__doc__:
+ print ' %s%s%s' %(GREY, v.__doc__, C_NORMAL)
+ else:
+ print
return True
-def write_dot_file(basename, edge_list, vertices=None, label=None, destdir=None,
- reformat_labels=True, directed=False, debug=None):
- from tempfile import NamedTemporaryFile
- if label:
- basename += '_' + label.translate(None, ', ') #fix DN, guid labels
- f = NamedTemporaryFile(suffix='.dot', prefix=basename + '_', delete=False, dir=destdir)
- if debug is not None:
- debug(f.name)
- graphname = ''.join(x for x in basename if x.isalnum())
- print >>f, '%s %s {' % ('digraph' if directed else 'graph', graphname)
- print >>f, 'label="%s";\nfontsize=20;' % (label or graphname)
- if vertices:
- for v in vertices:
- if reformat_labels:
- v = v.replace(',', '\\n')
- print >>f, '"%s";' % (v,)
- for a, b in edge_list:
- if reformat_labels:
- a = a.replace(',', '\\n')
- b = b.replace(',', '\\n')
- line = '->' if directed else '--'
- print >>f, '"%s" %s "%s";' % (a, line, b)
- print >>f, '}'
- f.close()
-
-
-
-class KCCGraphError(Exception):
- pass
-
-def verify_graph_complete(edges, vertices, edge_vertices):
- """The graph is complete, which is to say there is an edge between
- every pair of nodes."""
- for v in vertices:
- remotes = set()
- for a, b in edges:
- if a == v:
- remotes.add(b)
- elif b == v:
- remotes.add(a)
- if len(remotes) + 1 != len(vertices):
- raise KCCGraphError("graph is not fully connected")
-
-
-def verify_graph_connected(edges, vertices, edge_vertices):
- """There is a path between any two nodes."""
- if not edges:
- if len(vertices) <= 1:
- return
- raise KCCGraphError("disconnected vertices were found:\nvertices: %s\n edges: %s" %
- (sorted(vertices), sorted(edges)))
-
- remaining_edges = list(edges)
- reached = set(remaining_edges.pop())
- while True:
- doomed = []
- for i, e in enumerate(remaining_edges):
- a, b = e
- if a in reached:
- reached.add(b)
- doomed.append(i)
- elif b in reached:
- reached.add(a)
- doomed.append(i)
- if not doomed:
- break
- for i in reversed(doomed):
- del remaining_edges[i]
-
- if remaining_edges or reached != vertices:
- raise KCCGraphError("graph is not connected:\nvertices: %s\n edges: %s" %
- (sorted(vertices), sorted(edges)))
-
-
-
-def verify_graph_forest(edges, vertices, edge_vertices):
- """The graph contains no loops. A forest that is also connected is a
- tree."""
- trees = [set(e) for e in edges]
- while True:
- for a, b in itertools.combinations(trees, 2):
- intersection = a & b
- if intersection:
- if len(intersection) == 1:
- a |= b
- trees.remove(b)
- break
- else:
- raise KCCGraphError("there is a loop in the graph")
- else:
- # no break in itertools.combinations loop means no
- # further mergers, so we're done.
- #
- # XXX here we also know whether it is a tree or a
- # forest by len(trees) but the connected test already
- # tells us that.
- return
-
-def verify_graph_multi_edge_forest(edges, vertices, edge_vertices):
- """This allows a forest with duplicate edges. That is if multiple
- edges go between the same two vertices, they are treated as a
- single edge by this test.
-
- e.g.:
- o
- pass: o-o=o o=o (|) fail: o-o
- `o o `o'
- """
- unique_edges = set(edges)
- trees = [set(e) for e in unique_edges]
- while True:
- for a, b in itertools.combinations(trees, 2):
- intersection = a & b
- if intersection:
- if len(intersection) == 1:
- a |= b
- trees.remove(b)
- break
- else:
- raise KCCGraphError("there is a loop in the graph")
- else:
- return
-
-
-def verify_graph_forest_of_rings(edges, vertices, edge_vertices):
- """The graph should consist of clusters of node connected in rings,
- with the connections between the cdlusters forming a forest."""
- pass
-
-
-def verify_graph_no_lonely_vertices(edges, vertices, edge_vertices):
- """There are no vertices without edges."""
- lonely = vertices - edge_vertices
- if lonely:
- raise KCCGraphError("some vertices are not connected:\n%s" % '\n'.join(sorted(lonely)))
-
-
-def verify_graph_no_unknown_vertices(edges, vertices, edge_vertices):
- """The edge endpoints contain no vertices that are otherwise unknown."""
- unknown = edge_vertices - vertices
- if unknown:
- raise KCCGraphError("some edge vertices are seemingly unknown:\n%s" % '\n'.join(sorted(unknown)))
-
-
-def verify_graph_directed_double_ring(edges, vertices, edge_vertices):
- """Each node has at least two directed edges leaving it, and two
- arriving. The edges work in pairs that have the same end points
- but point in opposite directions. The pairs form a path that
- touches every vertex and form a loop.
-
- There might be other connections that *aren't* part of the ring.
- """
- #XXX possibly the 1 and 2 vertex cases are special cases.
- if not edges:
- return
- if len(edges) < 2* len(vertices):
- raise KCCGraphError("directed double ring requires at least twice as many edges as vertices")
-
- exits = {}
- for start, end in edges:
- s = exits.setdefault(start, [])
- s.append(end)
-
- try:
- #follow both paths at once -- they should be the same length
- #XXX there is probably a simpler way.
- forwards, backwards = exits[start]
- fprev, bprev = (start, start)
- f_path = [start]
- b_path = [start]
- for i in range(len(vertices)):
- a, b = exits[forwards]
- if a == fprev:
- fnext = b
- else:
- fnext = a
- f_path.append(forwards)
- fprev = forwards
- forwards = fnext
-
- a, b = exits[backwards]
- if a == bprev:
- bnext = b
- else:
- bnext = a
- b_path.append(backwards)
- bprev = backwards
- backwards = bnext
-
- except ValueError, e:
- raise KCCGraphError("wrong number of exits '%s'" % e)
-
- f_set = set(f_path)
- b_set = set(b_path)
-
- if (f_path != list(reversed(b_path)) or
- len(f_path) != len(f_set) + 1 or
- len(f_set) != len(vertices)):
- raise KCCGraphError("doesn't seem like a double ring to me!")
-
-
-def verify_graph_directed_double_ring_or_small(edges, vertices, edge_vertices):
- if len(vertices) < 3:
- return
- return verify_graph_directed_double_ring(edges, vertices, edge_vertices)
-
-
-
-def verify_graph(title, edges, vertices=None, directed=False, properties=(), fatal=True,
- debug=None):
- errors = []
- if debug is None:
- def debug(*args): pass
-
- debug("%sStarting verify_graph for %s%s%s" % (PURPLE, MAGENTA, title, C_NORMAL))
-
- properties = [x.replace(' ', '_') for x in properties]
-
- edge_vertices = set()
- for a, b in edges:
- edge_vertices.add(a)
- edge_vertices.add(b)
-
- if vertices is None:
- vertices = edge_vertices
- else:
- vertices = set(vertices)
- if vertices != edge_vertices:
- debug("vertices in edges don't match given vertices:\n %s != %s" %
- (sorted(edge_vertices), sorted(vertices)))
-
- for p in properties:
- fn = 'verify_graph_%s' % p
- try:
- f = globals()[fn]
- except KeyError:
- errors.append((p, "There is no verification check for '%s'" % p))
- try:
- f(edges, vertices, edge_vertices)
- debug(" %s%18s:%s verified!" % (DARK_GREEN, p, C_NORMAL))
- except KCCGraphError, e:
- errors.append((p, e))
-
- if errors:
- if fatal:
- raise KCCGraphError("The '%s' graph lacks the following properties:\n%s" %
- (title, '\n'.join('%s: %s' % x for x in errors)))
- debug(("%s%s%s FAILED:" % (MAGENTA, title, RED)))
- for p, e in errors:
- debug(" %18s: %s%s%s" %(p, DARK_YELLOW, e, RED))
- debug(C_NORMAL)
-
-
-
-def verify_and_dot(basename, edges, vertices=None, label=None, destdir=None,
- reformat_labels=True, directed=False, properties=(), fatal=True,
- debug=None, verify=True, dot_files=False):
-
- title = '%s %s' % (basename, label or '')
- if verify:
- verify_graph(title, edges, vertices, properties=properties, fatal=fatal,
- debug=debug)
- if dot_files:
- write_dot_file(basename, edges, vertices=vertices, label=label, destdir=destdir,
- reformat_labels=reformat_labels, directed=directed, debug=debug)
-
-def list_verify_tests():
- for k, v in sorted(globals().items()):
- if k.startswith('verify_graph_'):
- print k.replace('verify_graph_', '')
- if v.__doc__:
- print ' %s%s%s' %(GREY, v.__doc__, C_NORMAL)
- else:
- print
git.samba.org / nivanova / samba-autobuild / .git / commitdiff