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@nmz787
Last active Apr 5, 2017
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An attempt at making a point-to-point route solver for 3D grids, using graph reasoning through monosat
from collections import OrderedDict, defaultdict
import os
import sys
import subprocess
from copy import deepcopy
from monosat import *
from time import time
# enable using multiple levels of dict keys automatically, even if nested levels don't yet exist
NestedDict = lambda: defaultdict(NestedDict)
class SATGenerator(object):
def __init__(self, traces, maxx, maxy, maxz):
self.maxx = maxx
self.maxy = maxy
self.maxz = maxz
all_coords = [traces[t][io] for t in traces for io in traces[t]]
duped_coords = list(all_coords);
[duped_coords.remove(t) for t in set(all_coords)]
assert len(set(all_coords)) == len(all_coords), 'coords duplicated: {}'.format(duped_coords)
self.vars = {}
self.edge_vars = {}
self.edges_by_nodes = {}
self.nodes = {}
self.traces = traces
self.visited_neighbor_edges = []
self.reaches = []
self.setup_output()
self.create_vars()
self.create_clauses()
res = self.solve()
if(res):
self.parse_solution(res)
def setup_output(self):
self.m = Monosat()
self.m.setOutputFile('solver_out2')
self.m.init(' '.join([ '-conflict-min-cut', '-theory-order-vsids', '-decide-theories']))
#self.m.init('-kt-preserve-order -force-distance')
#self.m.init(' '.join( ['-verb=1', '-theory-order-vsids', '-vsids-both', '-decide-theories', '-no-decide-graph-rnd', '-lazy-maxflow-decisions', '-conflict-min-cut', '-conflict-min-cut-maxflow', '-reach-underapprox-cnf', '-adaptive-history-clear=5']))
self.g = Graph()
def create_vars(self):
# setup nodes
self.num_v = 0
self.grid_by_xyz = {} # OrderedDict()
for x in range(self.maxx):
ys = {} # OrderedDict()
for y in range(self.maxy):
zs = {} # OrderedDict()
for z in range(self.maxz):
v = self.node(('x {} y {} z {} node'.format(x, y, z), (x, y, z)))
zs[z] = {'node': v, 'edges': [], 'xyz': (x, y, z), 'edges_xyz': NestedDict()}
self.num_v += 1
ys[y] = zs
self.grid_by_xyz[x] = ys
# setup all possible edges
for x in range(self.maxx):
for y in range(self.maxy):
for z in range(self.maxz):
self._neighbor_edges(x, y, z)
def create_clauses(self):
# go through the traces, OR the start node edges, then setup reachability to the end node
self.start_end = []
ios_overall = []
for trace in self.traces:
ix, iy, iz = self.traces[trace]['input']
ox, oy, oz = self.traces[trace]['output']
self.start_end.append((ix, iy, iz))
self.start_end.append((ox, oy, oz))
input_node = self.grid_by_xyz[ix][iy][iz]
output_node = self.grid_by_xyz[ox][oy][oz]
ios_overall.append([input_node, output_node])
# only one of these edges is True
# self.clause(input_node['edges'])
# self._naive_mutex(input_node['edges'])
inp_circumferential_loc_nodes = self._get_circumferential_locs(ix, iy, iz)
inp_outward_edges = [self._node_edge_to(input_node, cn) for cn in inp_circumferential_loc_nodes]
assert sorted(input_node['edges'], key=lambda x: id(x)) == sorted(inp_outward_edges,
key=lambda x: id(x)), '{}\n{}'.format(
sorted(input_node['edges'], key=lambda x: id(x)), sorted(inp_outward_edges, key=lambda x: id(x)))
inp_inward_edges = [self._node_edge_to(cn, input_node) for cn in inp_circumferential_loc_nodes]
if any([(v in inp_inward_edges) for v in inp_outward_edges]):
raise Exception('some outward edges were also inward, gonna cause graph problems!')
#self.clause(inp_outward_edges + inp_inward_edges)
#self.clause(inp_outward_edges + inp_inward_edges)
#AssertNor(*inp_inward_edges)
#AssertAtMostOne(inp_outward_edges +inp_inward_edges)
#AssertAtMostOne(inp_inward_edges)
#AssertEqualPB(inp_outward_edges, 1)
#AssertEqualPB(inp_inward_edges, 0)
#AssertNor(inp_inward_edges)
# Assert(Not(inp_inward_edges))
#######
outp_circumferential_loc_nodes = self._get_circumferential_locs(ox, oy, oz)
outp_outward_edges = [self._node_edge_to(output_node, cn) for cn in outp_circumferential_loc_nodes]
outp_inward_edges = [self._node_edge_to(cn, output_node) for cn in outp_circumferential_loc_nodes]
if any([(v in outp_inward_edges) for v in outp_outward_edges]):
raise Exception('some outward edges were also inward, gonna cause graph problems!')
#self.clause(outp_inward_edges + outp_outward_edges)
#AssertNor(*outp_outward_edges)
#AssertAtMostOne(outp_inward_edges + outp_outward_edges)
#AssertAtMostOne(outp_outward_edges)
#AssertEqualPB(outp_inward_edges, 1)
# print(outp_outward_edges)
#AssertEqualPB(outp_outward_edges, 0)
#AssertNor(outp_outward_edges)
# self._naive_mutex([self._node_edge_to(cn, output_node) for cn in circumferential_loc_nodes])
# new var for the clause of reachability between two nodes (start and end)
# rv = self.var('reach {}'.format(trace))
# reach <graphID> node1 node2 var
# self.output.write('reach 0 {} {} {}\n'.format(ios[0]['node'], ios[1]['node'], rv))
inp_node = input_node['node']
outp_node = output_node['node']
rv = self.g.reaches(inp_node, outp_node)
self.reaches.append(rv)
# the var is True
#self.clause([rv])
Assert(rv)
if trace == 't4':
print('t4 dist 10')
#dist = self.g.distance_lt(inp_node, outp_node, 12)
#Assert(dist)
#rv = self.g.reaches(output_node['node'], input_node['node'])
# the var is True
#self.clause([Not(rv)])
#Assert(Not(rv))
#AssertNor(rv)
# # for every space
# all_edges = set()
numv = 0
p = one_percent = int(self.num_v / 100.0)
for x in range(self.maxx):
for y in range(self.maxy):
for z in range(self.maxz):
numv += 1
if (numv >= p):
p += one_percent
print('{} of {}'.format(numv, self.num_v))
# p = self.num_v
if (x, y, z) in self.start_end:
continue
# for e in self.grid_by_xyz[x][y][z]['edges']:
# all_edges.add(e)
# self._neighbor_constraint2(x,y,z)
for cl_node in self._get_circumferential_locs(x, y, z):
starting_edge = self._node_edge_to(self.grid_by_xyz[x][y][z], cl_node)
self._neighbor_constraint(self.grid_by_xyz[x][y][z], cl_node, starting_edge)
# for edge_vars_for_direction in zip(*locs):
# # allow only one trace's edge
# self._naive_mutex(edge_vars_for_direction)
# the following line should be handled by the neighbor clauses, falling like dominoes from the start edges
# self.clause(all_edges)
# _false = self.var('false'.format(trace))
# self.clause([Not(_false)])
# _true = self.var('true')
# self.clause([_true])
# # disallow an input to connect to any other trace's output
for ios in ios_overall:
inp = ios[0]
# get all other traces beside this current one
others = list(ios_overall);
others.remove(ios)
# get all other traces' outputs
other_outputs = [other_io[1] for other_io in others]
for other_out in other_outputs:
# self.output.write('reach 0 {} {} {}\n'.format(inp['node'], other_out['node'], _false))
rv = self.g.reaches(inp['node'], other_out['node'])
#self.clause([Not(rv)])
AssertNor(rv)
# self.output.write('acyclic 0 {}\n'.format(_true))
Assert(self.g.acyclic())
def solve(self):
print('num nodes {} num edges {} num vars {}'.format(len(self.nodes), len(self.edge_vars), self.num_v))
start_time = time()
result = Solve()
elapsed = time()-start_time
if(not result):
print("Constraints are UNSAT")
else:
print('Found solution in %d seconds'%(elapsed))
return result
def parse_solution(self, res):
""" for a given trace, walk all edges and save them in a grid for easy printing """
for rv in self.reaches:
#If the result is SAT, you can find the nodes that make up a satisfying path:
path_by_nodes = self.g.getPath(rv)
print("Satisfying path (as a list of nodes): " +str(path_by_nodes))
# find the longest trace name
l = ''
for trace in list(self.traces) + ['*']:
if len(trace) > len(l):
l = trace
# store the length of the longest trace name
l = len(l)
# open a new file to print the readable solution to
o = open('sol_out', 'w')
for trace in self.traces:
out_xyz = []
start = place = self.traces[trace]['input']
end = self.traces[trace]['output']
msg = 'trace: {} start: {} end: {}'.format(trace, start, end)
o.write('\n {}\n'.format(msg))
print(msg)
place = self.traces[trace]['input']
op = self.traces[trace]['output']
journey = []
branches = []
while place != op:
journey.append(place)
ix, iy, iz = place
try:
ns = [e for e in self.grid_by_xyz[ix][iy][iz]['edges'] if e.value() and self.edge_vars[e][1] not in journey]
n = ns[0]
branches += ns[1:]
except IndexError:
try:
n = branches.pop()
except IndexError:
print('branch ended!')
break #Sam: added this catch, to break in the case where branches is empty above.
place = self.edge_vars[n][1]
if (ix, iy, iz) != self.edge_vars[n][0]:
print('prev {} expected prev {}'.format((ix, iy, iz), self.edge_vars[n][0]))
jx,jy,jz = place
print('node in journey: {}'.format(self.grid_by_xyz[jx][jy][jz]['node']))
# now that we're done walking the graph, we can make a crude sort-of bitmap
for z in range(self.maxz):
o.write('Z {}\n'.format(z))
for x in range(self.maxx):
for y in range(self.maxy):
# print a * for start/end points
if (x, y, z) in [start, end]:
o.write('*{} '.format(' ' * (l - 1)))
# print the trace-name for points in a trace
elif (x, y, z) in journey: # self.trace_journeys[trace]['journey']:
o.write('{}{} '.format(trace, ' ' * (l - len(trace))))
# if a space is unused, print a 0
else:
o.write('0{} '.format(' ' * (l - 1)))
o.write('\n')
o.write('\n')
o.close()
def var(self, name):
v = Var()
self.vars[v] = name
return v
def node(self, name):
n = self.g.addNode()
self.nodes[n] = (name)
return n# len(self.nodes)
def clause(self, v_list):
#Assert(Or(*v_list))
AssertOr(*v_list) #Sam: changed this from Assert(Or(*v_list))
def _neighbor_edges(self, x, y, z):
n = self.grid_by_xyz[x][y][z]
circumferential_locs = self._get_circumferential_locs(x, y, z)
for cl in circumferential_locs:
ev = self._edge(n, cl)
n['edges'].append(ev)
xx, yy, zz = cl['xyz']
n['edges_xyz'][xx][yy][zz] = ev
def _node_edge_to(self, n, on):
x, y, z = on['xyz']
edge = n['edges_xyz'][x][y][z]
assert len([n['edges_xyz'][xx][yy][zz] for xx in n['edges_xyz'] for yy in n['edges_xyz'][xx] for zz in
n['edges_xyz'][xx][yy]]) == len(n['edges'])
return edge
def _neighbor_constraint(self, from_node, center_node, edge_came_from):
# if (from_node, center_node) in self.visited_neighbor_edges or (center_node, from_node) in self.visited_neighbor_edges:
# return False
# if center_node['xyz'] in [self.traces[t]['output'] for t in self.traces]:
# return False
# self.visited_neighbor_edges.append((from_node, center_node))
circumferential_loc_nodes = self._get_circumferential_locs(*center_node['xyz'])
if from_node not in circumferential_loc_nodes:
raise Exception('{} {}'.format(circumferential_loc_nodes, from_node))
assert self._node_edge_to(from_node, center_node) == edge_came_from, 'uh oh'
circumferential_loc_nodes.remove(from_node)
# if the edge_came_from is True, then one of the outgoing edges is True
outgoing_edges = [self._node_edge_to(center_node, n) for n in circumferential_loc_nodes]
self.clause([Not(edge_came_from)] + outgoing_edges)# + [self._node_edge_to(n, center_node) for n in circumferential_loc_nodes])
AssertAtMostOne(outgoing_edges)
# TODO why is the next line causing output to be weird?
#circumferential_loc_nodes = self._get_circumferential_locs(*center_node['xyz'])
#AssertAtMostOne([self._node_edge_to(center_node, n) for n in circumferential_loc_nodes])
#AssertAtMostOne([edge_came_from] + [self._node_edge_to(n, center_node) for n in circumferential_loc_nodes])
#AssertAtMostOne([self._node_edge_to(n, center_node) for n in circumferential_loc_nodes])
# Assert(Or(Not(v[1]), *es))
def _edge(self, _from, _to):
"""edge <GraphID> <from> <to> <CNF Variable> [weight]"""
# self.output.write('edge {} {} {} {} {}\n'.format(graph_id, _from, _to, v, w if w>1 else ''))
if (_from['node'], _to['node']) in self.edges_by_nodes:
raise Exception('we already saw this edge!')
v = self.g.addEdge(_from['node'], _to['node'])
self.edge_vars[v] = (_from['xyz'], _to['xyz'])
self.edges_by_nodes[(_from['node'], _to['node'])] = v
return v
def _get_circumferential_locs(self, x, y, z):
# up, down (in Z), left, right, ahead, behind (in-plane), diags
ensure = 2 + 4 + 4
# up, down (in Z), left, right, ahead, behind (in-plane)
ensure = 2 + 4
nvs = []
disallow_fortyfives = True
for xx in [x - 1, x, x + 1]:
if xx < 0 or xx >= self.maxx:
ensure = None
continue
for yy in [y - 1, y, y + 1]:
if yy < 0 or yy >= self.maxy:
ensure = None
continue
for zz in [z - 1, z, z + 1]:
if xx < 0 or xx >= self.maxx or yy < 0 or yy >= self.maxy or zz < 0 or zz >= self.maxz:
ensure = None
continue
# skip the center point (don't count the point passed into this method)
if x == xx and y == yy and z == zz:
continue
# restrict vias to vertical Z transitions only
# if Z is changing, AND x or y is too, we gotta skip it..
# Z can only change when going directly up or down
if zz != z and (xx != x or yy != y):
continue
# forty-five degree angles are disabled for now
# they can be enabled when diagonally crossing edges are disallowed
if disallow_fortyfives:
if abs(xx - x) == 1 and abs(yy - y) == 1:
continue
try:
nvs.append(self.grid_by_xyz[xx][yy][zz])
except:
print('{} {} {}'.format(xx, yy, zz))
raise
if ensure is not None:
assert len(nvs) == ensure, 'nvs was {}'.format(nvs)
return nvs
x=12
y=12
z=2
simple = False
if simple:
# make up some start and end points, to be placed within a grid of size: 20 x 20 x 2
traces = OrderedDict([('t1', {'input': (3, 3, 1),
'output': (10, 10, 0)}),
('t2', {'input': (0, 10, 0),
'output': (10, 1, 0)}),
('t3', {'input': (0, 0, 0),
'output': (10, 10, 1)}),
('t4', {'input': (1, 3, 0),
'output': (10, 4, 0)})])
else:
# make some inputs on the left, with outputs on the right (or in the other axis, top to bottom)
traces = OrderedDict()
do_y = False
if do_y:
for iy in range(y):
traces['t{}'.format(iy)] = {'input': (0,iy, 0), 'output': (x-1,iy, 0)}
else:
for ix in range(x):
traces['t{}'.format(ix)] = {'input': (ix,0, 0), 'output': (ix,y-1, 0)}
# traces = OrderedDict([('t1', {'input': (0, 0, 0),
# 'output': (2, 2, 0)})])
# pass the traces and the grid size, it begins to generate clauses and proceed to call the solver
SATGenerator(traces, maxx=x, maxy=y, maxz=z)
# SATGenerator(traces, maxx=3, maxy=3, maxz=1)
# diff pairs --
# if i am going forward, then buddy's candidate edges have to be parallel...
# OR if i am doing L shape, then my buddy can do an offset L shape
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