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+% -------------------------------------------------------------------------
+% Copyright (c) 2018 AT&T Intellectual Property
+%
+% Licensed under the Apache License, Version 2.0 (the "License");
+% you may not use this file except in compliance with the License.
+% You may obtain a copy of the License at
+%
+% http://www.apache.org/licenses/LICENSE-2.0
+%
+% Unless required by applicable law or agreed to in writing, software
+% distributed under the License is distributed on an "AS IS" BASIS,
+% WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+% See the License for the specific language governing permissions and
+% limitations under the License.
+%
+% -------------------------------------------------------------------------
+%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Parameters and its assertions
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% Number of cells/radios.
+int: NUM_NODES;
+
+% Maximum number of Physical Cell Identifiers to be assigned to the nodes.
+int: NUM_PCIS;
+
+% Number of edges between neighbor nodes. There is a edge (i,j) if and only
+% if nodes i and j are neighbors, i.e., an user equipment (UE) can make
+% handoff between i and j. Such edges are used to avoid **COLLISION**, i.e.,
+% to guarantee that nodes i and j have different PCIs.
+int: NUM_NEIGHBORS;
+
+% Each line represents an edge between direct neighbors as defined before.
+array[1..NUM_NEIGHBORS, 1..2] of int: NEIGHBORS;
+
+% Number of undirect neighbor pairs (j, k) such that both j and k are direct
+% neighbors of node i, i.e., (j, k) exits if and only if exists (i, j) and
+% (i, k). Nodes (i, k) can generate "confunsions" in the network if they have
+% the same PCI. Such edges are used to avoid/minimize **CONFUSIONS**.
+int: NUM_SECOND_LEVEL_NEIGHBORS;
+
+% Each line represents an edge between undirect neighbors as defined before.
+array[1..NUM_SECOND_LEVEL_NEIGHBORS, 1..2] of int: SECOND_LEVEL_NEIGHBORS;
+
+% Number of ignorable neighbor links. Such links can be ignored during
+% optimization if needed.
+int: NUM_IGNORABLE_NEIGHBOR_LINKS;
+
+% The links that can be ignored if needed. Each line represents the two ends
+% of the links, like the previous structures.
+array[1..NUM_IGNORABLE_NEIGHBOR_LINKS, 1..2] of int: IGNORABLE_NEIGHBOR_LINKS;
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Decision variables
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% Defines the PCI for each node.
+array[0..NUM_NODES-1] of var 0..NUM_PCIS-1: pci;
+
+array[1..NUM_IGNORABLE_NEIGHBOR_LINKS] of var 0..1: used_ignorables;
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Constraints
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% Direct neighbors must have different PCIs for avoid **COLLISION**.
+% Forced links.
+constraint
+forall(i in 1..NUM_NEIGHBORS, j in 1..NUM_IGNORABLE_NEIGHBOR_LINKS
+ where
+ NEIGHBORS[i, 1] != IGNORABLE_NEIGHBOR_LINKS[j, 1] \/
+ NEIGHBORS[i, 2] != IGNORABLE_NEIGHBOR_LINKS[j, 2]
+)(
+ pci[NEIGHBORS[i, 1]] != pci[NEIGHBORS[i, 2]]
+);
+
+
+% Ignorable links.
+constraint
+forall(i in 1..NUM_NEIGHBORS, j in 1..NUM_IGNORABLE_NEIGHBOR_LINKS
+ where
+ NEIGHBORS[i, 1] == IGNORABLE_NEIGHBOR_LINKS[j, 1] /\
+ NEIGHBORS[i, 2] == IGNORABLE_NEIGHBOR_LINKS[j, 2]
+)(
+ used_ignorables[j] >= bool2int(pci[NEIGHBORS[i, 1]] == pci[NEIGHBORS[i, 2]])
+);
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Objective function
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% Total number of confusions.
+var int: total_confusions =
+ sum([bool2int(pci[SECOND_LEVEL_NEIGHBORS[i, 1]] ==
+ pci[SECOND_LEVEL_NEIGHBORS[i, 2]])
+ | i in 1..NUM_SECOND_LEVEL_NEIGHBORS]);
+
+% Total number of used ignorables links.
+var int: total_used_ignorables = sum(used_ignorables);
+
+solve :: int_search(pci, smallest, indomain_min, complete)
+
+% Minimize the total number of confusions.
+%minimize total_confusions;
+
+% Minimize the total number of confusions first,
+% then the number of used ignorables links.
+minimize (2 * NUM_IGNORABLE_NEIGHBOR_LINKS * total_confusions) +
+ total_used_ignorables;
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Output
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+output
+["PCI assigment"] ++
+["\nnode,pci"] ++
+[
+ "\n" ++ show(node) ++ "," ++ show(pci[node])
+| node in 0..NUM_NODES-1
+] ++
+["\n\nTotal used ignorables links: " ++ show(total_used_ignorables)] ++
+["\nUsed ignorables links: "] ++
+[
+ "\n" ++ show(IGNORABLE_NEIGHBOR_LINKS[i, 1]) ++
+ "," ++ show(IGNORABLE_NEIGHBOR_LINKS[i, 2])
+ | i in 1..NUM_IGNORABLE_NEIGHBOR_LINKS where fix(used_ignorables[i] > 0)
+] ++
+["\n\nConfusions"] ++
+["\nTotal confusions: " ++ show(total_confusions)] ++
+["\nConfusion pairs"] ++
+[
+ "\n" ++ show(SECOND_LEVEL_NEIGHBORS[i, 1]) ++ "," ++
+ show(SECOND_LEVEL_NEIGHBORS[i, 2])
+ | i in 1..NUM_SECOND_LEVEL_NEIGHBORS where
+ fix(pci[SECOND_LEVEL_NEIGHBORS[i, 1]] == pci[SECOND_LEVEL_NEIGHBORS[i, 2]])
+]
+