def code_to_consumption_graph(self, consumption_graph: ConsumptionGraph,
code) -> ConsumptionGraph:
"""
this function take code that represent new graph and convert
it to that consumption_graph
the calculation of the properties of each agent is p[i]/2 from the end of arr belongs to the new agent
and len(arr)-p[i]/2 from the start of arr belongs to agent i
:param consumption_graph: the original graph
:param code:the code in form (x1,x2...xi) i = the number of agent in graph, xi in range(number of properties of
agent i in graph
:return: consumption_graph for that code
>>> v = [[40,30,20,10],[40,30,20,10],[40,30,20,10],[10,10,10,10]]
>>> gg = GraphGenerator(v)
>>> g = [[0,1,1,0],[1,0,0,0],[0,1,0,1]]
>>> cg = ConsumptionGraph(g)
>>> print(gg.code_to_consumption_graph(cg,(0,0,0)).get_graph())
[[0.0, 1, 1, 0.0], [1, 0.0, 0.0, 0.0], [0.0, 1, 0.0, 1], [0.0, 0.0, 0.0, 0.0]]
>>> print(gg.code_to_consumption_graph(cg,(4,1,3)).get_graph())
[[0.0, 0.0, 0.0, 0.0], [1, 0.0, 0.0, 0.0], [0.0, 1, 0.0, 0.0], [1, 1, 1, 1]]
>>> v1 = [[1,2,3,4],[8,7,6,5],[9,12,10,11],[1,2,3,4]]
>>> g1 = [[0,1,1,0],[1,0,0,0],[0,1,0,1]]
>>> gg = GraphGenerator(v1)
>>> cg = ConsumptionGraph(g1)
>>> print(gg.code_to_consumption_graph(cg,(2,3,2)).get_graph())
[[0.0, 1, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 1, 0.0, 0.0], [1, 0.0, 1, 1]]
>>> print(gg.code_to_consumption_graph(cg,(4,1,3)).get_graph())
[[0.0, 0.0, 0.0, 0.0], [1, 0.0, 0.0, 0.0], [0.0, 1, 0.0, 0.0], [1, 1, 1, 1]]
>>> print(gg.code_to_consumption_graph(cg,(3,1,1)).get_graph())
[[0.0, 1, 0.0, 0.0], [1, 0.0, 0.0, 0.0], [0.0, 1, 0.0, 1], [1, 1, 1, 1]]
>>> print(gg.code_to_consumption_graph(cg,(1,2,3)).get_graph())
[[0.0, 1, 1, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 1, 0.0, 0.0], [1, 1, 1, 1]]
>>> v1 = [[1,2,3,4],[8,7,6,5],[9,12,10,11],[1,4,3,2]]
>>> gg = GraphGenerator(v1)
>>> print(gg.code_to_consumption_graph(cg,(2,3,2)).get_graph())
[[0.0, 0.0, 1, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 1], [1, 1, 0.0, 0.0]]
"""
graph = consumption_graph.get_graph()
mat = np.zeros((len(graph) + 1, len(graph[0]))).tolist()
for i in range(len(graph)):
arr = self.valuation_ratios.create_the_value_ratio_for_2(
consumption_graph, i, len(graph))
num_of_properties = len(arr)
current_agent_properties = math.ceil(num_of_properties -
code[i] / 2)
new_agent_properties = math.ceil(code[i] / 2)
for j in range(current_agent_properties):
mat[i][arr[j][0]] = 1
for j in range(num_of_properties - new_agent_properties,
num_of_properties):
mat[len(graph)][int(arr[j][0])] = 1
return ConsumptionGraph(mat)
def add_agent(self, genneretor, i):
"""
this function get generator for all the the graph for i-1 agent
and generate all the graph for adding agent i
:param genneretor: generator for the all the graph for i-1 agents
:param i: the index for the new agent
:return: generator for the all the graph for i agents
>>> a = (0)
>>> matv = [[30,20,10],[20,15,10],[5,5,5]]
>>> gg = GraphGenerator(matv)
>>> gen = gg.add_agent(a,0)
>>> for g in gg.add_agent(gen,1):
... print(g.get_graph())
[[1, 1, 0.0], [0.0, 1, 1]]
[[1, 0.0, 0.0], [0.0, 1, 1]]
[[1, 0.0, 0.0], [1, 1, 1]]
"""
if (i == 0):
arr = []
# the first agent gets all the objects
arr.append([1] * len(self.valuation_matrix[0]))
yield ConsumptionGraph(arr)
else:
for g in genneretor:
for x in self.add_agent_to_graph(g):
yield x
def add_agent_to_graph(self, consumption_graph: ConsumptionGraph):
"""
:param consumption_graph: : some given ConsumptionGraph that represent agent and there properties
:return: generator for the all the graphs from adding agent i to the given graph
>>> matv = [[40,30,20],[40,30,20],[10,10,10]]
>>> graph = [[1,1,0],[0,1,1]]
>>> g = GraphGenerator(matv)
>>> cg = ConsumptionGraph(graph)
>>> for x in g.add_agent_to_graph(cg):
... print(x.get_graph())
[[1, 1, 0.0], [0.0, 1, 1], [0.0, 0.0, 1]]
[[1, 1, 0.0], [0.0, 1, 0.0], [0.0, 0.0, 1]]
[[1, 1, 0.0], [0.0, 1, 0.0], [0.0, 1, 1]]
[[1, 1, 0.0], [0.0, 1, 1], [0.0, 1, 0.0]]
[[1, 1, 0.0], [0.0, 1, 1], [0.0, 1, 1]]
[[1, 1, 0.0], [0.0, 1, 0.0], [0.0, 1, 1]]
[[1, 1, 0.0], [0.0, 1, 0.0], [0.0, 1, 1]]
[[1, 0.0, 0.0], [0.0, 1, 1], [0.0, 1, 0.0]]
[[1, 0.0, 0.0], [0.0, 1, 1], [0.0, 1, 1]]
[[1, 0.0, 0.0], [0.0, 1, 0.0], [0.0, 1, 1]]
[[1, 0.0, 0.0], [0.0, 1, 0.0], [0.0, 1, 1]]
[[1, 0.0, 0.0], [0.0, 1, 1], [1, 1, 0.0]]
[[1, 0.0, 0.0], [0.0, 1, 1], [1, 1, 1]]
[[1, 0.0, 0.0], [0.0, 1, 0.0], [1, 1, 1]]
[[1, 0.0, 0.0], [0.0, 1, 0.0], [1, 1, 1]]
>>> matv = [[40,30,20],[40,30,20],[10,10,10]]
>>> graph = [[1,1,1],[0,0,0]]
>>> g = GraphGenerator(matv)
>>> cg = ConsumptionGraph(graph)
>>> for x in g.add_agent_to_graph(cg):
... print(x.get_graph())
"""
for code in consumption_graph.generate_all_code():
g = self.code_to_consumption_graph(consumption_graph, code)
#anther adding!!!
if (g.is_prop(self.valuation_matrix)) and (
g.get_num_of_sharing() <= self.num_of_sharing_is_allowed):
# the fixing!!
#if (g.get_num_of_sharing() <= self.num_of_sharing_is_allowed):
yield g
def find_allocation_for_graph(self, consumption_graph: ConsumptionGraph):
"""
this function get a consumption graph and use cvxpy to solve
the convex problem to find a envy free allocation.
the condition for the convex problem is:
1) each alloc[i][j] >=0 - an agent cant get minus pesent
from some item
2) if consumption_graph[i][j] == 0 so alloc[i][j]= 0 .
if in the current consumption graph the agent i doesnt consume the item j
so in the allocation he is get 0% from this item
3) the envy free condition (by definition)
4) the sum of every column in the allocation == 1
each item divided exactly to 100 percent
and after solving the problem - check if the result are better from the
"min_sharing_allocation" (meaning if the current allocation as lass shering from "min_sharing_allocation")
and update it
:param consumption_graph: some given consumption graph
:return: update "min_sharing_allocation"
# the test are according to the result of ver 1 in GraphCheck
>>> v = [[5, 2, 1.5,1], [9, 1, 3,2.5], [10, 3, 2,4]]
>>> fefap =FairEnvyFreeAllocationProblem(v)
>>> g1 = [[1, 1, 0.0, 0.0], [1, 0.0, 1, 0.0], [1, 0.0, 0.0, 1]]
>>> g = ConsumptionGraph(g1)
>>> print(fefap.find_allocation_for_graph(g))
[[0.337 1. 0. 0. ]
[0.342 0. 1. 0. ]
[0.32 0. 0. 0.999]]
>>> g1 = [[1, 1, 0.0, 0.0], [1, 0.0, 1, 0.0], [1, 0.0, 0.0, 1]]
>>> g = ConsumptionGraph(g1)
>>> print(fefap.find_allocation_for_graph(g))
[[0.337 1. 0. 0. ]
[0.342 0. 1. 0. ]
[0.32 0. 0. 0.999]]
>>> g1 = [[1, 1, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [1, 0.0, 1, 1]]
>>> g = ConsumptionGraph(g1)
>>> print(fefap.find_allocation_for_graph(g))
None
>>> g1 = [[1, 1, 0.0, 0.0], [1, 0.0, 1, 1], [1, 0.0, 0.0, 0.0]]
>>> g = ConsumptionGraph(g1)
>>> print(fefap.find_allocation_for_graph(g))
[[0.302 0.999 0. 0. ]
[0.046 0. 0.999 1. ]
[0.651 0. 0. 0. ]]
>>> g1 = [[1, 1, 0.0, 0.0], [1, 0.0, 1, 1], [1, 0.0, 0.0, 1]]
>>> g = ConsumptionGraph(g1)
>>> print(fefap.find_allocation_for_graph(g))
[[0.322 1. 0. 0. ]
[0.251 0. 1. 0.332]
[0.425 0. 0. 0.667]]
>>> g1 = [[1, 1, 0.0, 0.0], [1, 0.0, 1, 1], [0.0, 0.0, 0.0, 0.0]]
>>> g = ConsumptionGraph(g1)
>>> print(fefap.find_allocation_for_graph(g))
None
>>> g1 = [[1, 1, 0.0, 0.0], [1, 0.0, 1, 0.0], [1, 0.0, 0.0, 1]]
>>> g = ConsumptionGraph(g1)
>>> print(fefap.find_allocation_for_graph(g))
[[0.337 1. 0. 0. ]
[0.342 0. 1. 0. ]
[0.32 0. 0. 0.999]]
"""
mat = cvxpy.Variable((self.num_of_agents, self.num_of_items))
constraints = []
# every var >=0 and if there is no edge the var is zero
# and envy_free condition
for i in range(self.num_of_agents):
agent_sum = 0
for j in range(self.num_of_items):
agent_sum += mat[i][j] * self.valuation[i][j]
if (consumption_graph.get_graph()[i][j] == 0):
constraints.append(mat[i][j] == 0)
else:
constraints.append(mat[i][j] >= 0)
anther_agent_sum = 0
for j in range(self.num_of_agents):
anther_agent_sum = 0
for k in range(self.num_of_items):
anther_agent_sum += mat[j][k] * self.valuation[i][k]
constraints.append(agent_sum >= anther_agent_sum)
# the sum of each column is 1 (the property on each object is 100%)
for i in range(self.num_of_items):
constraints.append(sum(mat[:, i]) == 1)
objective = cvxpy.Maximize(1)
prob = cvxpy.Problem(objective, constraints)
try:
prob.solve(solver="OSQP")
except cvxpy.SolverError:
prob.solve(solver="SCS")
if prob.status == 'optimal':
alloc = Allocation(mat.value)
alloc.round()
self.min_sharing_number = alloc.num_of_shering()
self.min_sharing_allocation = alloc.get_allocation()
self.find = True
# only for doctet:
return (mat.value)
def find_allocation_for_graph(self, consumption_graph: ConsumptionGraph):
"""
this function get a consumption graph and use cvxpy to solve
the convex problem to find a proportional allocation.
the condition for the convex problem is:
1) each alloc[i][j] >=0 - an agent cant get minus pesent
from some item
2) if consumption_graph[i][j] == 0 so alloc[i][j]= 0 .
if in the current consumption graph the agent i doesnt consume the item j
so in the allocation he is get 0% from this item
3) the proportional condition (by definition)
4) the sum of every column in the allocation == 1
each item divided exactly to 100 percent
and after solving the problem - check if the result are better from the
"min_sharing_allocation" (meaning if the current allocation as lass shering from "min_sharing_allocation")
and update it
:param consumption_graph: some given consumption graph
:return: update "min_sharing_allocation"
# the test are according to the result of ver 1 in GraphCheck
>>> v = [[1, 2, 3,4], [4, 5, 6,5], [7, 8, 9,6]]
>>> fpap =FairProportionalAllocationProblem(v)
>>> g1 = [[0.0, 0.0, 0.0, 1], [1, 1, 1, 1], [0.0, 0.0, 0.0, 1]]
>>> g = ConsumptionGraph(g1)
>>> print(fpap.find_allocation_for_graph(g))
None
>>> g1 = [[0.0, 0.0, 0.0, 1], [1, 1, 1, 1], [1, 0.0, 0.0, 1]]
>>> g = ConsumptionGraph(g1)
>>> print(fpap.find_allocation_for_graph(g))
None
>>> g1 = [[0.0, 0.0, 0.0, 1], [0.0, 1, 1, 1], [1, 0.0, 0.0, 1]]
>>> g = ConsumptionGraph(g1)
>>> print(fpap.find_allocation_for_graph(g))
None
>>> g1 = [[0.0, 0.0, 0.0, 1], [0.0, 1, 1, 1], [1, 1, 0.0, 1]]
>>> g = ConsumptionGraph(g1)
>>> print(fpap.find_allocation_for_graph(g))
[[0. 0. 0. 0.884]
[0. 0.464 1. 0.049]
[1. 0.535 0. 0.065]]
>>> g1 = [[0.0, 0.0, 0.0, 1], [0.0, 0.0, 1, 1], [1, 1, 0.0, 1]]
>>> g = ConsumptionGraph(g1)
>>> print(fpap.find_allocation_for_graph(g))
[[0. 0. 0. 0.842]
[0. 0. 0.999 0.147]
[1. 1. 0. 0.01 ]]
>>> g1 = [[0.0, 0.0, 0.0, 1], [0.0, 0.0, 1, 1], [1, 1, 1, 1]]
>>> g = ConsumptionGraph(g1)
>>> print(fpap.find_allocation_for_graph(g))
[[0. 0. 0. 0.836]
[0. 0. 0.994 0.149]
[1. 1. 0.005 0.013]]
>>> g1 = [[0.0, 0.0, 0.0, 1], [0.0, 1, 1, 1], [1, 0.0, 0.0, 0.0]]
>>> g = ConsumptionGraph(g1)
>>> print(fpap.find_allocation_for_graph(g))
None
>>> g1 = [[0.0, 0.0, 0.0, 1], [0.0, 1, 1, 1], [1, 1, 0.0, 0.0]]
>>> g = ConsumptionGraph(g1)
>>> print(fpap.find_allocation_for_graph(g))
[[0. 0. 0. 0.856]
[0. 0.471 1. 0.143]
[1. 0.528 0. 0. ]]
"""
if (consumption_graph.get_num_of_sharing() ==
self.graph_generator.num_of_sharing_is_allowed):
mat = cvxpy.Variable((self.num_of_agents, self.num_of_items))
constraints = []
# every var >=0 and if there is no edge the var is zero
# and proportional condition
for i in range(self.num_of_agents):
count = 0
for j in range(self.num_of_items):
if (consumption_graph.get_graph()[i][j] == 0):
constraints.append(mat[i][j] == 0)
else:
constraints.append(mat[i][j] >= 0)
count += mat[i][j] * self.valuation[i][j]
constraints.append(
count >= sum(self.valuation[i]) / len(self.valuation))
# the sum of each column is 1 (the property on each object is 100%)
for i in range(self.num_of_items):
constraints.append(sum(mat[:, i]) == 1)
objective = cvxpy.Maximize(1)
prob = cvxpy.Problem(objective, constraints)
try:
prob.solve(solver="OSQP")
except cvxpy.SolverError:
prob.solve(solver="SCS")
if prob.status == 'optimal':
# prob.solve(solver="SCS") # Returns the optimal value. prob.solve(solver="SCS")
# if not (prob.status == 'infeasible'):
alloc = Allocation(mat.value)
alloc.round()
self.min_sharing_number = alloc.num_of_shering()
self.min_sharing_allocation = alloc.get_allocation()
self.find = True
# only for doctet:
return (mat.value)