0
4
0
... | ... |
@@ -139,9 +139,10 @@ |
139 | 139 |
TEMPLATE_DIGRAPH_TYPEDEFS(GR); |
140 | 140 |
|
141 | 141 |
typedef std::vector<int> IntVector; |
142 |
typedef std::vector<char> BoolVector; |
|
143 | 142 |
typedef std::vector<Value> ValueVector; |
144 | 143 |
typedef std::vector<Cost> CostVector; |
144 |
typedef std::vector<char> BoolVector; |
|
145 |
// Note: vector<char> is used instead of vector<bool> for efficiency reasons |
|
145 | 146 |
|
146 | 147 |
private: |
147 | 148 |
|
... | ... |
@@ -798,15 +799,15 @@ |
798 | 799 |
// Initialize delta value |
799 | 800 |
if (_factor > 1) { |
800 | 801 |
// With scaling |
801 |
Value max_sup = 0, max_dem = 0; |
|
802 |
for (int i = 0; i != _node_num; ++i) { |
|
802 |
Value max_sup = 0, max_dem = 0, max_cap = 0; |
|
803 |
for (int i = 0; i != _root; ++i) { |
|
803 | 804 |
Value ex = _excess[i]; |
804 | 805 |
if ( ex > max_sup) max_sup = ex; |
805 | 806 |
if (-ex > max_dem) max_dem = -ex; |
807 |
int last_out = _first_out[i+1] - 1; |
|
808 |
for (int j = _first_out[i]; j != last_out; ++j) { |
|
809 |
if (_res_cap[j] > max_cap) max_cap = _res_cap[j]; |
|
806 | 810 |
} |
807 |
Value max_cap = 0; |
|
808 |
for (int j = 0; j != _res_arc_num; ++j) { |
|
809 |
if (_res_cap[j] > max_cap) max_cap = _res_cap[j]; |
|
810 | 811 |
} |
811 | 812 |
max_sup = std::min(std::min(max_sup, max_dem), max_cap); |
812 | 813 |
for (_delta = 1; 2 * _delta <= max_sup; _delta *= 2) ; |
... | ... |
@@ -201,10 +201,11 @@ |
201 | 201 |
TEMPLATE_DIGRAPH_TYPEDEFS(GR); |
202 | 202 |
|
203 | 203 |
typedef std::vector<int> IntVector; |
204 |
typedef std::vector<char> BoolVector; |
|
205 | 204 |
typedef std::vector<Value> ValueVector; |
206 | 205 |
typedef std::vector<Cost> CostVector; |
207 | 206 |
typedef std::vector<LargeCost> LargeCostVector; |
207 |
typedef std::vector<char> BoolVector; |
|
208 |
// Note: vector<char> is used instead of vector<bool> for efficiency reasons |
|
208 | 209 |
|
209 | 210 |
private: |
210 | 211 |
|
... | ... |
@@ -248,6 +249,7 @@ |
248 | 249 |
// Parameters of the problem |
249 | 250 |
bool _have_lower; |
250 | 251 |
Value _sum_supply; |
252 |
int _sup_node_num; |
|
251 | 253 |
|
252 | 254 |
// Data structures for storing the digraph |
253 | 255 |
IntNodeMap _node_id; |
... | ... |
@@ -276,6 +278,12 @@ |
276 | 278 |
LargeCost _epsilon; |
277 | 279 |
int _alpha; |
278 | 280 |
|
281 |
IntVector _buckets; |
|
282 |
IntVector _bucket_next; |
|
283 |
IntVector _bucket_prev; |
|
284 |
IntVector _rank; |
|
285 |
int _max_rank; |
|
286 |
|
|
279 | 287 |
// Data for a StaticDigraph structure |
280 | 288 |
typedef std::pair<int, int> IntPair; |
281 | 289 |
StaticDigraph _sgr; |
... | ... |
@@ -828,6 +836,11 @@ |
828 | 836 |
} |
829 | 837 |
} |
830 | 838 |
|
839 |
_sup_node_num = 0; |
|
840 |
for (NodeIt n(_graph); n != INVALID; ++n) { |
|
841 |
if (sup[n] > 0) ++_sup_node_num; |
|
842 |
} |
|
843 |
|
|
831 | 844 |
// Find a feasible flow using Circulation |
832 | 845 |
Circulation<Digraph, ConstMap<Arc, Value>, ValueArcMap, ValueNodeMap> |
833 | 846 |
circ(_graph, low, cap, sup); |
... | ... |
@@ -862,7 +875,7 @@ |
862 | 875 |
} |
863 | 876 |
for (int a = _first_out[_root]; a != _res_arc_num; ++a) { |
864 | 877 |
int ra = _reverse[a]; |
865 |
_res_cap[a] = |
|
878 |
_res_cap[a] = 0; |
|
866 | 879 |
_res_cap[ra] = 0; |
867 | 880 |
_cost[a] = 0; |
868 | 881 |
_cost[ra] = 0; |
... | ... |
@@ -877,6 +890,13 @@ |
877 | 890 |
// Maximum path length for partial augment |
878 | 891 |
const int MAX_PATH_LENGTH = 4; |
879 | 892 |
|
893 |
// Initialize data structures for buckets |
|
894 |
_max_rank = _alpha * _res_node_num; |
|
895 |
_buckets.resize(_max_rank); |
|
896 |
_bucket_next.resize(_res_node_num + 1); |
|
897 |
_bucket_prev.resize(_res_node_num + 1); |
|
898 |
_rank.resize(_res_node_num + 1); |
|
899 |
|
|
880 | 900 |
// Execute the algorithm |
881 | 901 |
switch (method) { |
882 | 902 |
case PUSH: |
... | ... |
@@ -916,51 +936,23 @@ |
916 | 936 |
} |
917 | 937 |
} |
918 | 938 |
|
919 |
/// Execute the algorithm performing augment and relabel operations |
|
920 |
void startAugment(int max_length = std::numeric_limits<int>::max()) { |
|
921 |
// Paramters for heuristics |
|
922 |
const int BF_HEURISTIC_EPSILON_BOUND = 1000; |
|
923 |
const int BF_HEURISTIC_BOUND_FACTOR = 3; |
|
924 |
|
|
925 |
// Perform cost scaling phases |
|
926 |
IntVector pred_arc(_res_node_num); |
|
927 |
std::vector<int> path_nodes; |
|
928 |
for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ? |
|
929 |
1 : _epsilon / _alpha ) |
|
930 |
{ |
|
931 |
// "Early Termination" heuristic: use Bellman-Ford algorithm |
|
932 |
// to check if the current flow is optimal |
|
933 |
if (_epsilon <= BF_HEURISTIC_EPSILON_BOUND) { |
|
934 |
_arc_vec.clear(); |
|
935 |
_cost_vec.clear(); |
|
936 |
for (int j = 0; j != _res_arc_num; ++j) { |
|
937 |
if (_res_cap[j] > 0) { |
|
938 |
_arc_vec.push_back(IntPair(_source[j], _target[j])); |
|
939 |
_cost_vec.push_back(_cost[j] + 1); |
|
940 |
} |
|
941 |
} |
|
942 |
_sgr.build(_res_node_num, _arc_vec.begin(), _arc_vec.end()); |
|
943 |
|
|
944 |
BellmanFord<StaticDigraph, LargeCostArcMap> bf(_sgr, _cost_map); |
|
945 |
bf.init(0); |
|
946 |
bool done = false; |
|
947 |
int K = int(BF_HEURISTIC_BOUND_FACTOR * sqrt(_res_node_num)); |
|
948 |
for (int i = 0; i < K && !done; ++i) |
|
949 |
done = bf.processNextWeakRound(); |
|
950 |
if (done) break; |
|
951 |
} |
|
952 |
|
|
939 |
// Initialize a cost scaling phase |
|
940 |
void initPhase() { |
|
953 | 941 |
// Saturate arcs not satisfying the optimality condition |
954 |
for (int a = 0; a != _res_arc_num; ++a) { |
|
955 |
if (_res_cap[a] > 0 && |
|
956 |
|
|
942 |
for (int u = 0; u != _res_node_num; ++u) { |
|
943 |
int last_out = _first_out[u+1]; |
|
944 |
LargeCost pi_u = _pi[u]; |
|
945 |
for (int a = _first_out[u]; a != last_out; ++a) { |
|
946 |
int v = _target[a]; |
|
947 |
if (_res_cap[a] > 0 && _cost[a] + pi_u - _pi[v] < 0) { |
|
957 | 948 |
Value delta = _res_cap[a]; |
958 |
_excess[_source[a]] -= delta; |
|
959 |
_excess[_target[a]] += delta; |
|
949 |
_excess[u] -= delta; |
|
950 |
_excess[v] += delta; |
|
960 | 951 |
_res_cap[a] = 0; |
961 | 952 |
_res_cap[_reverse[a]] += delta; |
962 | 953 |
} |
963 | 954 |
} |
955 |
} |
|
964 | 956 |
|
965 | 957 |
// Find active nodes (i.e. nodes with positive excess) |
966 | 958 |
for (int u = 0; u != _res_node_num; ++u) { |
... | ... |
@@ -971,6 +963,146 @@ |
971 | 963 |
for (int u = 0; u != _res_node_num; ++u) { |
972 | 964 |
_next_out[u] = _first_out[u]; |
973 | 965 |
} |
966 |
} |
|
967 |
|
|
968 |
// Early termination heuristic |
|
969 |
bool earlyTermination() { |
|
970 |
const double EARLY_TERM_FACTOR = 3.0; |
|
971 |
|
|
972 |
// Build a static residual graph |
|
973 |
_arc_vec.clear(); |
|
974 |
_cost_vec.clear(); |
|
975 |
for (int j = 0; j != _res_arc_num; ++j) { |
|
976 |
if (_res_cap[j] > 0) { |
|
977 |
_arc_vec.push_back(IntPair(_source[j], _target[j])); |
|
978 |
_cost_vec.push_back(_cost[j] + 1); |
|
979 |
} |
|
980 |
} |
|
981 |
_sgr.build(_res_node_num, _arc_vec.begin(), _arc_vec.end()); |
|
982 |
|
|
983 |
// Run Bellman-Ford algorithm to check if the current flow is optimal |
|
984 |
BellmanFord<StaticDigraph, LargeCostArcMap> bf(_sgr, _cost_map); |
|
985 |
bf.init(0); |
|
986 |
bool done = false; |
|
987 |
int K = int(EARLY_TERM_FACTOR * std::sqrt(double(_res_node_num))); |
|
988 |
for (int i = 0; i < K && !done; ++i) { |
|
989 |
done = bf.processNextWeakRound(); |
|
990 |
} |
|
991 |
return done; |
|
992 |
} |
|
993 |
|
|
994 |
// Global potential update heuristic |
|
995 |
void globalUpdate() { |
|
996 |
int bucket_end = _root + 1; |
|
997 |
|
|
998 |
// Initialize buckets |
|
999 |
for (int r = 0; r != _max_rank; ++r) { |
|
1000 |
_buckets[r] = bucket_end; |
|
1001 |
} |
|
1002 |
Value total_excess = 0; |
|
1003 |
for (int i = 0; i != _res_node_num; ++i) { |
|
1004 |
if (_excess[i] < 0) { |
|
1005 |
_rank[i] = 0; |
|
1006 |
_bucket_next[i] = _buckets[0]; |
|
1007 |
_bucket_prev[_buckets[0]] = i; |
|
1008 |
_buckets[0] = i; |
|
1009 |
} else { |
|
1010 |
total_excess += _excess[i]; |
|
1011 |
_rank[i] = _max_rank; |
|
1012 |
} |
|
1013 |
} |
|
1014 |
if (total_excess == 0) return; |
|
1015 |
|
|
1016 |
// Search the buckets |
|
1017 |
int r = 0; |
|
1018 |
for ( ; r != _max_rank; ++r) { |
|
1019 |
while (_buckets[r] != bucket_end) { |
|
1020 |
// Remove the first node from the current bucket |
|
1021 |
int u = _buckets[r]; |
|
1022 |
_buckets[r] = _bucket_next[u]; |
|
1023 |
|
|
1024 |
// Search the incomming arcs of u |
|
1025 |
LargeCost pi_u = _pi[u]; |
|
1026 |
int last_out = _first_out[u+1]; |
|
1027 |
for (int a = _first_out[u]; a != last_out; ++a) { |
|
1028 |
int ra = _reverse[a]; |
|
1029 |
if (_res_cap[ra] > 0) { |
|
1030 |
int v = _source[ra]; |
|
1031 |
int old_rank_v = _rank[v]; |
|
1032 |
if (r < old_rank_v) { |
|
1033 |
// Compute the new rank of v |
|
1034 |
LargeCost nrc = (_cost[ra] + _pi[v] - pi_u) / _epsilon; |
|
1035 |
int new_rank_v = old_rank_v; |
|
1036 |
if (nrc < LargeCost(_max_rank)) |
|
1037 |
new_rank_v = r + 1 + int(nrc); |
|
1038 |
|
|
1039 |
// Change the rank of v |
|
1040 |
if (new_rank_v < old_rank_v) { |
|
1041 |
_rank[v] = new_rank_v; |
|
1042 |
_next_out[v] = _first_out[v]; |
|
1043 |
|
|
1044 |
// Remove v from its old bucket |
|
1045 |
if (old_rank_v < _max_rank) { |
|
1046 |
if (_buckets[old_rank_v] == v) { |
|
1047 |
_buckets[old_rank_v] = _bucket_next[v]; |
|
1048 |
} else { |
|
1049 |
_bucket_next[_bucket_prev[v]] = _bucket_next[v]; |
|
1050 |
_bucket_prev[_bucket_next[v]] = _bucket_prev[v]; |
|
1051 |
} |
|
1052 |
} |
|
1053 |
|
|
1054 |
// Insert v to its new bucket |
|
1055 |
_bucket_next[v] = _buckets[new_rank_v]; |
|
1056 |
_bucket_prev[_buckets[new_rank_v]] = v; |
|
1057 |
_buckets[new_rank_v] = v; |
|
1058 |
} |
|
1059 |
} |
|
1060 |
} |
|
1061 |
} |
|
1062 |
|
|
1063 |
// Finish search if there are no more active nodes |
|
1064 |
if (_excess[u] > 0) { |
|
1065 |
total_excess -= _excess[u]; |
|
1066 |
if (total_excess <= 0) break; |
|
1067 |
} |
|
1068 |
} |
|
1069 |
if (total_excess <= 0) break; |
|
1070 |
} |
|
1071 |
|
|
1072 |
// Relabel nodes |
|
1073 |
for (int u = 0; u != _res_node_num; ++u) { |
|
1074 |
int k = std::min(_rank[u], r); |
|
1075 |
if (k > 0) { |
|
1076 |
_pi[u] -= _epsilon * k; |
|
1077 |
_next_out[u] = _first_out[u]; |
|
1078 |
} |
|
1079 |
} |
|
1080 |
} |
|
1081 |
|
|
1082 |
/// Execute the algorithm performing augment and relabel operations |
|
1083 |
void startAugment(int max_length = std::numeric_limits<int>::max()) { |
|
1084 |
// Paramters for heuristics |
|
1085 |
const int EARLY_TERM_EPSILON_LIMIT = 1000; |
|
1086 |
const double GLOBAL_UPDATE_FACTOR = 3.0; |
|
1087 |
|
|
1088 |
const int global_update_freq = int(GLOBAL_UPDATE_FACTOR * |
|
1089 |
(_res_node_num + _sup_node_num * _sup_node_num)); |
|
1090 |
int next_update_limit = global_update_freq; |
|
1091 |
|
|
1092 |
int relabel_cnt = 0; |
|
1093 |
|
|
1094 |
// Perform cost scaling phases |
|
1095 |
std::vector<int> path; |
|
1096 |
for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ? |
|
1097 |
1 : _epsilon / _alpha ) |
|
1098 |
{ |
|
1099 |
// Early termination heuristic |
|
1100 |
if (_epsilon <= EARLY_TERM_EPSILON_LIMIT) { |
|
1101 |
if (earlyTermination()) break; |
|
1102 |
} |
|
1103 |
|
|
1104 |
// Initialize current phase |
|
1105 |
initPhase(); |
|
974 | 1106 |
|
975 | 1107 |
// Perform partial augment and relabel operations |
976 | 1108 |
while (true) { |
... | ... |
@@ -981,46 +1113,44 @@ |
981 | 1113 |
} |
982 | 1114 |
if (_active_nodes.size() == 0) break; |
983 | 1115 |
int start = _active_nodes.front(); |
984 |
path_nodes.clear(); |
|
985 |
path_nodes.push_back(start); |
|
986 | 1116 |
|
987 | 1117 |
// Find an augmenting path from the start node |
1118 |
path.clear(); |
|
988 | 1119 |
int tip = start; |
989 |
while (_excess[tip] >= 0 && |
|
990 |
int(path_nodes.size()) <= max_length) { |
|
1120 |
while (_excess[tip] >= 0 && int(path.size()) < max_length) { |
|
991 | 1121 |
int u; |
992 |
LargeCost min_red_cost, rc; |
|
993 |
int last_out = _sum_supply < 0 ? |
|
994 |
|
|
1122 |
LargeCost min_red_cost, rc, pi_tip = _pi[tip]; |
|
1123 |
int last_out = _first_out[tip+1]; |
|
995 | 1124 |
for (int a = _next_out[tip]; a != last_out; ++a) { |
996 |
if (_res_cap[a] > 0 && |
|
997 |
_cost[a] + _pi[_source[a]] - _pi[_target[a]] < 0) { |
|
998 | 1125 |
u = _target[a]; |
999 |
|
|
1126 |
if (_res_cap[a] > 0 && _cost[a] + pi_tip - _pi[u] < 0) { |
|
1127 |
path.push_back(a); |
|
1000 | 1128 |
_next_out[tip] = a; |
1001 | 1129 |
tip = u; |
1002 |
path_nodes.push_back(tip); |
|
1003 | 1130 |
goto next_step; |
1004 | 1131 |
} |
1005 | 1132 |
} |
1006 | 1133 |
|
1007 | 1134 |
// Relabel tip node |
1008 |
min_red_cost = std::numeric_limits<LargeCost>::max() |
|
1135 |
min_red_cost = std::numeric_limits<LargeCost>::max(); |
|
1136 |
if (tip != start) { |
|
1137 |
int ra = _reverse[path.back()]; |
|
1138 |
min_red_cost = _cost[ra] + pi_tip - _pi[_target[ra]]; |
|
1139 |
} |
|
1009 | 1140 |
for (int a = _first_out[tip]; a != last_out; ++a) { |
1010 |
rc = _cost[a] + |
|
1141 |
rc = _cost[a] + pi_tip - _pi[_target[a]]; |
|
1011 | 1142 |
if (_res_cap[a] > 0 && rc < min_red_cost) { |
1012 | 1143 |
min_red_cost = rc; |
1013 | 1144 |
} |
1014 | 1145 |
} |
1015 | 1146 |
_pi[tip] -= min_red_cost + _epsilon; |
1016 |
|
|
1017 |
// Reset the next arc of tip |
|
1018 | 1147 |
_next_out[tip] = _first_out[tip]; |
1148 |
++relabel_cnt; |
|
1019 | 1149 |
|
1020 | 1150 |
// Step back |
1021 | 1151 |
if (tip != start) { |
1022 |
path_nodes.pop_back(); |
|
1023 |
tip = path_nodes.back(); |
|
1152 |
tip = _source[path.back()]; |
|
1153 |
path.pop_back(); |
|
1024 | 1154 |
} |
1025 | 1155 |
|
1026 | 1156 |
next_step: ; |
... | ... |
@@ -1028,11 +1158,11 @@ |
1028 | 1158 |
|
1029 | 1159 |
// Augment along the found path (as much flow as possible) |
1030 | 1160 |
Value delta; |
1031 |
int u, v = path_nodes.front(), pa; |
|
1032 |
for (int i = 1; i < int(path_nodes.size()); ++i) { |
|
1161 |
int pa, u, v = start; |
|
1162 |
for (int i = 0; i != int(path.size()); ++i) { |
|
1163 |
pa = path[i]; |
|
1033 | 1164 |
u = v; |
1034 |
v = path_nodes[i]; |
|
1035 |
pa = pred_arc[v]; |
|
1165 |
v = _target[pa]; |
|
1036 | 1166 |
delta = std::min(_res_cap[pa], _excess[u]); |
1037 | 1167 |
_res_cap[pa] -= delta; |
1038 | 1168 |
_res_cap[_reverse[pa]] += delta; |
... | ... |
@@ -1041,6 +1171,12 @@ |
1041 | 1171 |
if (_excess[v] > 0 && _excess[v] <= delta) |
1042 | 1172 |
_active_nodes.push_back(v); |
1043 | 1173 |
} |
1174 |
|
|
1175 |
// Global update heuristic |
|
1176 |
if (relabel_cnt >= next_update_limit) { |
|
1177 |
globalUpdate(); |
|
1178 |
next_update_limit += global_update_freq; |
|
1179 |
} |
|
1044 | 1180 |
} |
1045 | 1181 |
} |
1046 | 1182 |
} |
... | ... |
@@ -1048,98 +1184,70 @@ |
1048 | 1184 |
/// Execute the algorithm performing push and relabel operations |
1049 | 1185 |
void startPush() { |
1050 | 1186 |
// Paramters for heuristics |
1051 |
const int BF_HEURISTIC_EPSILON_BOUND = 1000; |
|
1052 |
const int BF_HEURISTIC_BOUND_FACTOR = 3; |
|
1187 |
const int EARLY_TERM_EPSILON_LIMIT = 1000; |
|
1188 |
const double GLOBAL_UPDATE_FACTOR = 2.0; |
|
1189 |
|
|
1190 |
const int global_update_freq = int(GLOBAL_UPDATE_FACTOR * |
|
1191 |
(_res_node_num + _sup_node_num * _sup_node_num)); |
|
1192 |
int next_update_limit = global_update_freq; |
|
1193 |
|
|
1194 |
int relabel_cnt = 0; |
|
1053 | 1195 |
|
1054 | 1196 |
// Perform cost scaling phases |
1055 | 1197 |
BoolVector hyper(_res_node_num, false); |
1198 |
LargeCostVector hyper_cost(_res_node_num); |
|
1056 | 1199 |
for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ? |
1057 | 1200 |
1 : _epsilon / _alpha ) |
1058 | 1201 |
{ |
1059 |
// "Early Termination" heuristic: use Bellman-Ford algorithm |
|
1060 |
// to check if the current flow is optimal |
|
1061 |
if (_epsilon <= BF_HEURISTIC_EPSILON_BOUND) { |
|
1062 |
_arc_vec.clear(); |
|
1063 |
_cost_vec.clear(); |
|
1064 |
for (int j = 0; j != _res_arc_num; ++j) { |
|
1065 |
if (_res_cap[j] > 0) { |
|
1066 |
_arc_vec.push_back(IntPair(_source[j], _target[j])); |
|
1067 |
_cost_vec.push_back(_cost[j] + 1); |
|
1068 |
} |
|
1069 |
} |
|
1070 |
_sgr.build(_res_node_num, _arc_vec.begin(), _arc_vec.end()); |
|
1071 |
|
|
1072 |
BellmanFord<StaticDigraph, LargeCostArcMap> bf(_sgr, _cost_map); |
|
1073 |
bf.init(0); |
|
1074 |
bool done = false; |
|
1075 |
int K = int(BF_HEURISTIC_BOUND_FACTOR * sqrt(_res_node_num)); |
|
1076 |
for (int i = 0; i < K && !done; ++i) |
|
1077 |
done = bf.processNextWeakRound(); |
|
1078 |
if (done) break; |
|
1202 |
// Early termination heuristic |
|
1203 |
if (_epsilon <= EARLY_TERM_EPSILON_LIMIT) { |
|
1204 |
if (earlyTermination()) break; |
|
1079 | 1205 |
} |
1080 | 1206 |
|
1081 |
// Saturate arcs not satisfying the optimality condition |
|
1082 |
for (int a = 0; a != _res_arc_num; ++a) { |
|
1083 |
if (_res_cap[a] > 0 && |
|
1084 |
_cost[a] + _pi[_source[a]] - _pi[_target[a]] < 0) { |
|
1085 |
Value delta = _res_cap[a]; |
|
1086 |
_excess[_source[a]] -= delta; |
|
1087 |
_excess[_target[a]] += delta; |
|
1088 |
_res_cap[a] = 0; |
|
1089 |
_res_cap[_reverse[a]] += delta; |
|
1090 |
} |
|
1091 |
} |
|
1092 |
|
|
1093 |
// Find active nodes (i.e. nodes with positive excess) |
|
1094 |
for (int u = 0; u != _res_node_num; ++u) { |
|
1095 |
if (_excess[u] > 0) _active_nodes.push_back(u); |
|
1096 |
} |
|
1097 |
|
|
1098 |
// Initialize the next arcs |
|
1099 |
for (int u = 0; u != _res_node_num; ++u) { |
|
1100 |
_next_out[u] = _first_out[u]; |
|
1101 |
|
|
1207 |
// Initialize current phase |
|
1208 |
initPhase(); |
|
1102 | 1209 |
|
1103 | 1210 |
// Perform push and relabel operations |
1104 | 1211 |
while (_active_nodes.size() > 0) { |
1105 |
LargeCost min_red_cost, rc; |
|
1212 |
LargeCost min_red_cost, rc, pi_n; |
|
1106 | 1213 |
Value delta; |
1107 | 1214 |
int n, t, a, last_out = _res_arc_num; |
1108 | 1215 |
|
1216 |
next_node: |
|
1109 | 1217 |
// Select an active node (FIFO selection) |
1110 |
next_node: |
|
1111 | 1218 |
n = _active_nodes.front(); |
1112 |
last_out = _sum_supply < 0 ? |
|
1113 |
_first_out[n+1] : _first_out[n+1] - 1; |
|
1219 |
last_out = _first_out[n+1]; |
|
1220 |
pi_n = _pi[n]; |
|
1114 | 1221 |
|
1115 | 1222 |
// Perform push operations if there are admissible arcs |
1116 | 1223 |
if (_excess[n] > 0) { |
1117 | 1224 |
for (a = _next_out[n]; a != last_out; ++a) { |
1118 | 1225 |
if (_res_cap[a] > 0 && |
1119 |
_cost[a] + |
|
1226 |
_cost[a] + pi_n - _pi[_target[a]] < 0) { |
|
1120 | 1227 |
delta = std::min(_res_cap[a], _excess[n]); |
1121 | 1228 |
t = _target[a]; |
1122 | 1229 |
|
1123 | 1230 |
// Push-look-ahead heuristic |
1124 | 1231 |
Value ahead = -_excess[t]; |
1125 |
int last_out_t = _sum_supply < 0 ? |
|
1126 |
_first_out[t+1] : _first_out[t+1] - 1; |
|
1232 |
int last_out_t = _first_out[t+1]; |
|
1233 |
LargeCost pi_t = _pi[t]; |
|
1127 | 1234 |
for (int ta = _next_out[t]; ta != last_out_t; ++ta) { |
1128 | 1235 |
if (_res_cap[ta] > 0 && |
1129 |
_cost[ta] + |
|
1236 |
_cost[ta] + pi_t - _pi[_target[ta]] < 0) |
|
1130 | 1237 |
ahead += _res_cap[ta]; |
1131 | 1238 |
if (ahead >= delta) break; |
1132 | 1239 |
} |
1133 | 1240 |
if (ahead < 0) ahead = 0; |
1134 | 1241 |
|
1135 | 1242 |
// Push flow along the arc |
1136 |
if (ahead < delta) { |
|
1243 |
if (ahead < delta && !hyper[t]) { |
|
1137 | 1244 |
_res_cap[a] -= ahead; |
1138 | 1245 |
_res_cap[_reverse[a]] += ahead; |
1139 | 1246 |
_excess[n] -= ahead; |
1140 | 1247 |
_excess[t] += ahead; |
1141 | 1248 |
_active_nodes.push_front(t); |
1142 | 1249 |
hyper[t] = true; |
1250 |
hyper_cost[t] = _cost[a] + pi_n - pi_t; |
|
1143 | 1251 |
_next_out[n] = a; |
1144 | 1252 |
goto next_node; |
1145 | 1253 |
} else { |
... | ... |
@@ -1162,18 +1270,18 @@ |
1162 | 1270 |
|
1163 | 1271 |
// Relabel the node if it is still active (or hyper) |
1164 | 1272 |
if (_excess[n] > 0 || hyper[n]) { |
1165 |
min_red_cost = |
|
1273 |
min_red_cost = hyper[n] ? -hyper_cost[n] : |
|
1274 |
std::numeric_limits<LargeCost>::max(); |
|
1166 | 1275 |
for (int a = _first_out[n]; a != last_out; ++a) { |
1167 |
rc = _cost[a] + |
|
1276 |
rc = _cost[a] + pi_n - _pi[_target[a]]; |
|
1168 | 1277 |
if (_res_cap[a] > 0 && rc < min_red_cost) { |
1169 | 1278 |
min_red_cost = rc; |
1170 | 1279 |
} |
1171 | 1280 |
} |
1172 | 1281 |
_pi[n] -= min_red_cost + _epsilon; |
1282 |
_next_out[n] = _first_out[n]; |
|
1173 | 1283 |
hyper[n] = false; |
1174 |
|
|
1175 |
// Reset the next arc |
|
1176 |
|
|
1284 |
++relabel_cnt; |
|
1177 | 1285 |
} |
1178 | 1286 |
|
1179 | 1287 |
// Remove nodes that are not active nor hyper |
... | ... |
@@ -1183,6 +1291,14 @@ |
1183 | 1291 |
!hyper[_active_nodes.front()] ) { |
1184 | 1292 |
_active_nodes.pop_front(); |
1185 | 1293 |
} |
1294 |
|
|
1295 |
// Global update heuristic |
|
1296 |
if (relabel_cnt >= next_update_limit) { |
|
1297 |
globalUpdate(); |
|
1298 |
for (int u = 0; u != _res_node_num; ++u) |
|
1299 |
hyper[u] = false; |
|
1300 |
next_update_limit += global_update_freq; |
|
1301 |
} |
|
1186 | 1302 |
} |
1187 | 1303 |
} |
1188 | 1304 |
} |
... | ... |
@@ -144,10 +144,11 @@ |
144 | 144 |
TEMPLATE_DIGRAPH_TYPEDEFS(GR); |
145 | 145 |
|
146 | 146 |
typedef std::vector<int> IntVector; |
147 |
typedef std::vector<char> CharVector; |
|
148 | 147 |
typedef std::vector<double> DoubleVector; |
149 | 148 |
typedef std::vector<Value> ValueVector; |
150 | 149 |
typedef std::vector<Cost> CostVector; |
150 |
typedef std::vector<char> BoolVector; |
|
151 |
// Note: vector<char> is used instead of vector<bool> for efficiency reasons |
|
151 | 152 |
|
152 | 153 |
private: |
153 | 154 |
|
... | ... |
@@ -198,7 +199,7 @@ |
198 | 199 |
IntArcMap _arc_idf; |
199 | 200 |
IntArcMap _arc_idb; |
200 | 201 |
IntVector _first_out; |
201 |
|
|
202 |
BoolVector _forward; |
|
202 | 203 |
IntVector _source; |
203 | 204 |
IntVector _target; |
204 | 205 |
IntVector _reverse; |
... | ... |
@@ -962,8 +963,8 @@ |
962 | 963 |
// Contruct auxiliary data vectors |
963 | 964 |
DoubleVector pi(_res_node_num, 0.0); |
964 | 965 |
IntVector level(_res_node_num); |
965 |
CharVector reached(_res_node_num); |
|
966 |
CharVector processed(_res_node_num); |
|
966 |
BoolVector reached(_res_node_num); |
|
967 |
BoolVector processed(_res_node_num); |
|
967 | 968 |
IntVector pred_node(_res_node_num); |
968 | 969 |
IntVector pred_arc(_res_node_num); |
969 | 970 |
std::vector<int> stack(_res_node_num); |
... | ... |
@@ -164,9 +164,10 @@ |
164 | 164 |
TEMPLATE_DIGRAPH_TYPEDEFS(GR); |
165 | 165 |
|
166 | 166 |
typedef std::vector<int> IntVector; |
167 |
typedef std::vector<char> CharVector; |
|
168 | 167 |
typedef std::vector<Value> ValueVector; |
169 | 168 |
typedef std::vector<Cost> CostVector; |
169 |
typedef std::vector<char> BoolVector; |
|
170 |
// Note: vector<char> is used instead of vector<bool> for efficiency reasons |
|
170 | 171 |
|
171 | 172 |
// State constants for arcs |
172 | 173 |
enum ArcStateEnum { |
... | ... |
@@ -213,8 +214,8 @@ |
213 | 214 |
IntVector _succ_num; |
214 | 215 |
IntVector _last_succ; |
215 | 216 |
IntVector _dirty_revs; |
216 |
CharVector _forward; |
|
217 |
CharVector _state; |
|
217 |
BoolVector _forward; |
|
218 |
BoolVector _state; |
|
218 | 219 |
int _root; |
219 | 220 |
|
220 | 221 |
// Temporary data used in the current pivot iteration |
... | ... |
@@ -245,7 +246,7 @@ |
245 | 246 |
const IntVector &_source; |
246 | 247 |
const IntVector &_target; |
247 | 248 |
const CostVector &_cost; |
248 |
const |
|
249 |
const BoolVector &_state; |
|
249 | 250 |
const CostVector &_pi; |
250 | 251 |
int &_in_arc; |
251 | 252 |
int _search_arc_num; |
... | ... |
@@ -266,7 +267,7 @@ |
266 | 267 |
// Find next entering arc |
267 | 268 |
bool findEnteringArc() { |
268 | 269 |
Cost c; |
269 |
for (int e = _next_arc; e |
|
270 |
for (int e = _next_arc; e != _search_arc_num; ++e) { |
|
270 | 271 |
c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
271 | 272 |
if (c < 0) { |
272 | 273 |
_in_arc = e; |
... | ... |
@@ -274,7 +275,7 @@ |
274 | 275 |
return true; |
275 | 276 |
} |
276 | 277 |
} |
277 |
for (int e = 0; e |
|
278 |
for (int e = 0; e != _next_arc; ++e) { |
|
278 | 279 |
c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
279 | 280 |
if (c < 0) { |
280 | 281 |
_in_arc = e; |
... | ... |
@@ -297,7 +298,7 @@ |
297 | 298 |
const IntVector &_source; |
298 | 299 |
const IntVector &_target; |
299 | 300 |
const CostVector &_cost; |
300 |
const |
|
301 |
const BoolVector &_state; |
|
301 | 302 |
const CostVector &_pi; |
302 | 303 |
int &_in_arc; |
303 | 304 |
int _search_arc_num; |
... | ... |
@@ -314,7 +315,7 @@ |
314 | 315 |
// Find next entering arc |
315 | 316 |
bool findEnteringArc() { |
316 | 317 |
Cost c, min = 0; |
317 |
for (int e = 0; e |
|
318 |
for (int e = 0; e != _search_arc_num; ++e) { |
|
318 | 319 |
c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
319 | 320 |
if (c < min) { |
320 | 321 |
min = c; |
... | ... |
@@ -336,7 +337,7 @@ |
336 | 337 |
const IntVector &_source; |
337 | 338 |
const IntVector &_target; |
338 | 339 |
const CostVector &_cost; |
339 |
const |
|
340 |
const BoolVector &_state; |
|
340 | 341 |
const CostVector &_pi; |
341 | 342 |
int &_in_arc; |
342 | 343 |
int _search_arc_num; |
... | ... |
@@ -355,7 +356,7 @@ |
355 | 356 |
_next_arc(0) |
356 | 357 |
{ |
357 | 358 |
// The main parameters of the pivot rule |
358 |
const double BLOCK_SIZE_FACTOR = |
|
359 |
const double BLOCK_SIZE_FACTOR = 1.0; |
|
359 | 360 |
const int MIN_BLOCK_SIZE = 10; |
360 | 361 |
|
361 | 362 |
_block_size = std::max( int(BLOCK_SIZE_FACTOR * |
... | ... |
@@ -368,7 +369,7 @@ |
368 | 369 |
Cost c, min = 0; |
369 | 370 |
int cnt = _block_size; |
370 | 371 |
int e; |
371 |
for (e = _next_arc; e |
|
372 |
for (e = _next_arc; e != _search_arc_num; ++e) { |
|
372 | 373 |
c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
373 | 374 |
if (c < min) { |
374 | 375 |
min = c; |
... | ... |
@@ -379,7 +380,7 @@ |
379 | 380 |
cnt = _block_size; |
380 | 381 |
} |
381 | 382 |
} |
382 |
for (e = 0; e |
|
383 |
for (e = 0; e != _next_arc; ++e) { |
|
383 | 384 |
c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
384 | 385 |
if (c < min) { |
385 | 386 |
min = c; |
... | ... |
@@ -409,7 +410,7 @@ |
409 | 410 |
const IntVector &_source; |
410 | 411 |
const IntVector &_target; |
411 | 412 |
const CostVector &_cost; |
412 |
const |
|
413 |
const BoolVector &_state; |
|
413 | 414 |
const CostVector &_pi; |
414 | 415 |
int &_in_arc; |
415 | 416 |
int _search_arc_num; |
... | ... |
@@ -470,7 +471,7 @@ |
470 | 471 |
// Major iteration: build a new candidate list |
471 | 472 |
min = 0; |
472 | 473 |
_curr_length = 0; |
473 |
for (e = _next_arc; e |
|
474 |
for (e = _next_arc; e != _search_arc_num; ++e) { |
|
474 | 475 |
c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
475 | 476 |
if (c < 0) { |
476 | 477 |
_candidates[_curr_length++] = e; |
... | ... |
@@ -481,7 +482,7 @@ |
481 | 482 |
if (_curr_length == _list_length) goto search_end; |
482 | 483 |
} |
483 | 484 |
} |
484 |
for (e = 0; e |
|
485 |
for (e = 0; e != _next_arc; ++e) { |
|
485 | 486 |
c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
486 | 487 |
if (c < 0) { |
487 | 488 |
_candidates[_curr_length++] = e; |
... | ... |
@@ -512,7 +513,7 @@ |
512 | 513 |
const IntVector &_source; |
513 | 514 |
const IntVector &_target; |
514 | 515 |
const CostVector &_cost; |
515 |
const |
|
516 |
const BoolVector &_state; |
|
516 | 517 |
const CostVector &_pi; |
517 | 518 |
int &_in_arc; |
518 | 519 |
int _search_arc_num; |
... | ... |
@@ -565,7 +566,7 @@ |
565 | 566 |
bool findEnteringArc() { |
566 | 567 |
// Check the current candidate list |
567 | 568 |
int e; |
568 |
for (int i = 0; i |
|
569 |
for (int i = 0; i != _curr_length; ++i) { |
|
569 | 570 |
e = _candidates[i]; |
570 | 571 |
_cand_cost[e] = _state[e] * |
571 | 572 |
(_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
... | ... |
@@ -578,7 +579,7 @@ |
578 | 579 |
int cnt = _block_size; |
579 | 580 |
int limit = _head_length; |
580 | 581 |
|
581 |
for (e = _next_arc; e |
|
582 |
for (e = _next_arc; e != _search_arc_num; ++e) { |
|
582 | 583 |
_cand_cost[e] = _state[e] * |
583 | 584 |
(_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
584 | 585 |
if (_cand_cost[e] < 0) { |
... | ... |
@@ -590,7 +591,7 @@ |
590 | 591 |
cnt = _block_size; |
591 | 592 |
} |
592 | 593 |
} |
593 |
for (e = 0; e |
|
594 |
for (e = 0; e != _next_arc; ++e) { |
|
594 | 595 |
_cand_cost[e] = _state[e] * |
595 | 596 |
(_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
596 | 597 |
if (_cand_cost[e] < 0) { |
... | ... |
@@ -1360,7 +1361,7 @@ |
1360 | 1361 |
} |
1361 | 1362 |
|
1362 | 1363 |
// Update _rev_thread using the new _thread values |
1363 |
for (int i = 0; i |
|
1364 |
for (int i = 0; i != int(_dirty_revs.size()); ++i) { |
|
1364 | 1365 |
u = _dirty_revs[i]; |
1365 | 1366 |
_rev_thread[_thread[u]] = u; |
1366 | 1367 |
} |
... | ... |
@@ -1432,6 +1433,100 @@ |
1432 | 1433 |
} |
1433 | 1434 |
} |
1434 | 1435 |
|
1436 |
// Heuristic initial pivots |
|
1437 |
bool initialPivots() { |
|
1438 |
Value curr, total = 0; |
|
1439 |
std::vector<Node> supply_nodes, demand_nodes; |
|
1440 |
for (NodeIt u(_graph); u != INVALID; ++u) { |
|
1441 |
curr = _supply[_node_id[u]]; |
|
1442 |
if (curr > 0) { |
|
1443 |
total += curr; |
|
1444 |
supply_nodes.push_back(u); |
|
1445 |
} |
|
1446 |
else if (curr < 0) { |
|
1447 |
demand_nodes.push_back(u); |
|
1448 |
} |
|
1449 |
} |
|
1450 |
if (_sum_supply > 0) total -= _sum_supply; |
|
1451 |
if (total <= 0) return true; |
|
1452 |
|
|
1453 |
IntVector arc_vector; |
|
1454 |
if (_sum_supply >= 0) { |
|
1455 |
if (supply_nodes.size() == 1 && demand_nodes.size() == 1) { |
|
1456 |
// Perform a reverse graph search from the sink to the source |
|
1457 |
typename GR::template NodeMap<bool> reached(_graph, false); |
|
1458 |
Node s = supply_nodes[0], t = demand_nodes[0]; |
|
1459 |
std::vector<Node> stack; |
|
1460 |
reached[t] = true; |
|
1461 |
stack.push_back(t); |
|
1462 |
while (!stack.empty()) { |
|
1463 |
Node u, v = stack.back(); |
|
1464 |
stack.pop_back(); |
|
1465 |
if (v == s) break; |
|
1466 |
for (InArcIt a(_graph, v); a != INVALID; ++a) { |
|
1467 |
if (reached[u = _graph.source(a)]) continue; |
|
1468 |
int j = _arc_id[a]; |
|
1469 |
if (_cap[j] >= total) { |
|
1470 |
arc_vector.push_back(j); |
|
1471 |
reached[u] = true; |
|
1472 |
stack.push_back(u); |
|
1473 |
} |
|
1474 |
} |
|
1475 |
} |
|
1476 |
} else { |
|
1477 |
// Find the min. cost incomming arc for each demand node |
|
1478 |
for (int i = 0; i != int(demand_nodes.size()); ++i) { |
|
1479 |
Node v = demand_nodes[i]; |
|
1480 |
Cost c, min_cost = std::numeric_limits<Cost>::max(); |
|
1481 |
Arc min_arc = INVALID; |
|
1482 |
for (InArcIt a(_graph, v); a != INVALID; ++a) { |
|
1483 |
c = _cost[_arc_id[a]]; |
|
1484 |
if (c < min_cost) { |
|
1485 |
min_cost = c; |
|
1486 |
min_arc = a; |
|
1487 |
} |
|
1488 |
} |
|
1489 |
if (min_arc != INVALID) { |
|
1490 |
arc_vector.push_back(_arc_id[min_arc]); |
|
1491 |
} |
|
1492 |
} |
|
1493 |
} |
|
1494 |
} else { |
|
1495 |
// Find the min. cost outgoing arc for each supply node |
|
1496 |
for (int i = 0; i != int(supply_nodes.size()); ++i) { |
|
1497 |
Node u = supply_nodes[i]; |
|
1498 |
Cost c, min_cost = std::numeric_limits<Cost>::max(); |
|
1499 |
Arc min_arc = INVALID; |
|
1500 |
for (OutArcIt a(_graph, u); a != INVALID; ++a) { |
|
1501 |
c = _cost[_arc_id[a]]; |
|
1502 |
if (c < min_cost) { |
|
1503 |
min_cost = c; |
|
1504 |
min_arc = a; |
|
1505 |
} |
|
1506 |
} |
|
1507 |
if (min_arc != INVALID) { |
|
1508 |
arc_vector.push_back(_arc_id[min_arc]); |
|
1509 |
} |
|
1510 |
} |
|
1511 |
} |
|
1512 |
|
|
1513 |
// Perform heuristic initial pivots |
|
1514 |
for (int i = 0; i != int(arc_vector.size()); ++i) { |
|
1515 |
in_arc = arc_vector[i]; |
|
1516 |
if (_state[in_arc] * (_cost[in_arc] + _pi[_source[in_arc]] - |
|
1517 |
_pi[_target[in_arc]]) >= 0) continue; |
|
1518 |
findJoinNode(); |
|
1519 |
bool change = findLeavingArc(); |
|
1520 |
if (delta >= MAX) return false; |
|
1521 |
changeFlow(change); |
|
1522 |
if (change) { |
|
1523 |
updateTreeStructure(); |
|
1524 |
updatePotential(); |
|
1525 |
} |
|
1526 |
} |
|
1527 |
return true; |
|
1528 |
} |
|
1529 |
|
|
1435 | 1530 |
// Execute the algorithm |
1436 | 1531 |
ProblemType start(PivotRule pivot_rule) { |
1437 | 1532 |
// Select the pivot rule implementation |
... | ... |
@@ -1454,6 +1549,9 @@ |
1454 | 1549 |
ProblemType start() { |
1455 | 1550 |
PivotRuleImpl pivot(*this); |
1456 | 1551 |
|
1552 |
// Perform heuristic initial pivots |
|
1553 |
if (!initialPivots()) return UNBOUNDED; |
|
1554 |
|
|
1457 | 1555 |
// Execute the Network Simplex algorithm |
1458 | 1556 |
while (pivot.findEnteringArc()) { |
1459 | 1557 |
findJoinNode(); |
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