def low_degree_orientation(g, weight=None):
res = TFGraph(g.nodes)
if weight is None:
weight = defaultdict(int)
deglist = []
buckets = []
for v in g:
d = g.degree(v) + weight[v]
# Flexible deglist[v] = d
if v < len(deglist):
deglist[v] = d
else:
deglist.extend([0 for x in range(len(deglist), v)])
deglist.insert(v, d)
# Flexible buckets[d].add(v)
if d < len(buckets):
buckets[d].add(v)
else:
buckets.extend([set() for x in range(len(buckets), d)])
buckets.insert(d,{v})
seen = set()
for i in xrange(0, len(g)):
d = 0
while len(buckets[d]) == 0:
d += 1
v = buckets[d].pop()
for u in g.neighbours(v):
if u in seen:
continue
d = deglist[u]
buckets[d].remove(u)
buckets[d-1].add(u)
deglist[u] -= 1
# Orient edges towards v
res.add_arc(u, v, 1)
seen.add(v)
return res
def low_degree_orientation(g, weight=None):
res = TFGraph(g.nodes)
if weight is None:
weight = defaultdict( int )
deglist = []
buckets = []
for v in g:
d = g.degree(v) + weight[v]
# Flexible deglist[v] = d
if v < len(deglist):
deglist[v] = d
else:
deglist.extend([0 for x in range(len(deglist), v)])
deglist.insert( v, d )
# Flexible buckets[d].add(v)
if d < len(buckets):
buckets[d].add(v)
else:
buckets.extend([set() for x in range(len(buckets), d)])
buckets.insert(d,{v})
seen = set()
for i in xrange(0, len(g)):
d = 0
while len(buckets[d]) == 0:
d += 1
v = buckets[d].pop()
for u in g.neighbours(v):
if u in seen:
continue
d = deglist[u]
buckets[d].remove(u)
buckets[d-1].add(u)
deglist[u] -= 1
# Orient edges towards v
res.add_arc(u, v, 1)
seen.add(v)
return res
def sandpile_orientation(g, weight=None):
res = TFGraph(g.nodes)
if len(res) == 0:
return res
if weight is None:
weight = defaultdict( int )
deglist = []
buckets = []
for v in g:
d = g.degree(v) + weight[v]
# Flexible deglist[v] = d
if v < len(deglist):
deglist[v] = d
else:
deglist.extend([0 for x in range(len(deglist), v)])
deglist.insert( v, d )
# Flexible buckets[d].add(v)
if d < len(buckets):
buckets[d].add(v)
else:
buckets.extend([set() for x in range(len(buckets), d)])
buckets.insert(d,{v})
seen = set()
for i in xrange(0, len(g)):
d = 0
while len(buckets[d]) == 0:
d += 1
v = buckets[d].pop()
for u in g.neighbours(v):
if u in seen:
continue
d = deglist[u]
buckets[d].remove(u)
buckets[d-1].add(u)
deglist[u] -= 1
# Orient edges towards v
res.add_arc(u, v, 1)
seen.add(v)
while True:
topple = []
forbidden = set()
for v in res:
if v in forbidden:
continue
d = res.in_degree(v) + weight[v]
cand = None
candd = d-2
for w, _ in res.in_neighbours(v):
if w in forbidden:
continue
if res.in_degree(w) + weight[w] <= candd:
cand = w
candd = res.in_degree(w)+weight[w]
if cand is not None:
topple.append((cand, v))
if len(topple) == 0:
break
for v, w in topple:
res.remove_arc(v, w)
res.add_arc(w, v, 1)
return res
