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fix some steiner tree comments and layout
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@GroteGnoom
GroteGnoom committed Dec 9, 2023
1 parent b9d8df3 commit d363c9c
Showing 1 changed file with 85 additions and 30 deletions.
115 changes: 85 additions & 30 deletions src/paths/steiner.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -44,9 +44,14 @@ typedef std::map<std::set<igraph_integer_t>, igraph_integer_t> dictionary;
* Populates the subsetMap data structure as well.
*
*/
static igraph_error_t generateSubsets(const igraph_vector_int_t *steinerTerminals, igraph_integer_t n, igraph_integer_t graphsize, dictionary &subsetMap, std::set<int_set> &allSubsets) {
static igraph_error_t generateSubsets(
const igraph_vector_int_t *steinerTerminals, igraph_integer_t n, igraph_integer_t graphsize,
dictionary &subsetMap, std::set<int_set> &allSubsets)
{
if (n > sizeof(igraph_integer_t) * 8 - 2) {
IGRAPH_ERROR("igraph_integer_overflow detected. The given number of terminals is more than what the computer can handle.", IGRAPH_EINVAL);
IGRAPH_ERROR(
"igraph_integer_overflow detected. "
"The given number of terminals is more than what the computer can handle.", IGRAPH_EINVAL);
}
igraph_integer_t count = ((igraph_integer_t)1 << n);
igraph_integer_t subsetIndex = graphsize;
Expand Down Expand Up @@ -163,7 +168,7 @@ static int_set fetchSetsBasedonIndex(igraph_integer_t index, const dictionary &s
* Time complexity: O( 3^k ∗ V + 2^k ∗ V^2 + V∗(V+E) ∗ log(V) )
* where V and E are the number of vertices and edges
* and k is the number of Steiner terminals.
* It is recommended that V &lt;= 50 and k &lt; 11.
* It is recommended that V <= 50 and k <= 11.
*
* \sa \ref igraph_minimum_spanning_tree(), \ref igraph_spanner()
*/
Expand Down Expand Up @@ -222,7 +227,9 @@ igraph_error_t igraph_steiner_dreyfus_wagner(
IGRAPH_VECTOR_INT_INIT_FINALLY(&vertices, 0);
IGRAPH_VECTOR_INT_INIT_FINALLY(&edges_res, 0);

IGRAPH_CHECK(igraph_get_shortest_path_dijkstra(graph, &vertices, &edges_res, VECTOR(*terminals)[0], VECTOR(*terminals)[1], pweights, IGRAPH_ALL));
IGRAPH_CHECK(igraph_get_shortest_path_dijkstra(
graph, &vertices, &edges_res, VECTOR(*terminals)[0],
VECTOR(*terminals)[1], pweights, IGRAPH_ALL));
igraph_integer_t tree_size = igraph_vector_int_size(&edges_res);

for (igraph_integer_t i = 0; i < tree_size; i++) {
Expand Down Expand Up @@ -261,15 +268,17 @@ igraph_error_t igraph_steiner_dreyfus_wagner(
igraph_integer_t component_id = VECTOR(membership)[VECTOR(*terminals)[0]];
for (igraph_integer_t i = 1; i < no_of_terminals; i++) {
if (VECTOR(membership)[VECTOR(*terminals)[i]] != component_id) {
IGRAPH_ERROR("Not all Steiner terminals are in the same connected component.", IGRAPH_EINVAL);
IGRAPH_ERROR(
"Not all Steiner terminals are in the same connected component.",
IGRAPH_EINVAL);
}
}
}

igraph_vector_int_destroy(&membership);
IGRAPH_FINALLY_CLEAN(1);
}
/* When every vertex is a Steiner terminal, the probably reduces to
/* When every vertex is a Steiner terminal, the problem reduces to
* finding a minimum spanning tree.
*/
if (no_of_terminals == no_of_nodes) {
Expand All @@ -291,16 +300,20 @@ igraph_error_t igraph_steiner_dreyfus_wagner(
igraph_matrix_t distance;

if (igraph_vector_size(pweights) != no_of_edges) {
IGRAPH_ERRORF("Weight vector length does not match %" IGRAPH_PRId "vec size and %" IGRAPH_PRId "edges.", IGRAPH_FAILURE, igraph_vector_size(weights), no_of_edges);
IGRAPH_ERRORF(
"Weight vector length does not match %" IGRAPH_PRId "vec size and %" IGRAPH_PRId "edges.",
IGRAPH_FAILURE, igraph_vector_size(weights), no_of_edges);
}
IGRAPH_CHECK(igraph_matrix_init(&distance, no_of_nodes, no_of_nodes));
IGRAPH_FINALLY(igraph_matrix_destroy, &distance);

/*
* Compute distances between all pairs of vertices. The Dreyfus - Wagner algorithm needs complete graph information
* Compute distances between all pairs of vertices.
* The Dreyfus - Wagner algorithm needs complete graph information
* hence this step is necessary.
*/
IGRAPH_CHECK(igraph_distances_dijkstra(graph, &distance, igraph_vss_all(), igraph_vss_all(), pweights, IGRAPH_ALL));
IGRAPH_CHECK(igraph_distances_dijkstra(
graph, &distance, igraph_vss_all(), igraph_vss_all(), pweights, IGRAPH_ALL));

IGRAPH_CHECK(igraph_vector_int_init_copy(&steiner_terminals_copy, terminals));
IGRAPH_FINALLY(igraph_vector_int_destroy, &steiner_terminals_copy);
Expand All @@ -311,17 +324,27 @@ igraph_error_t igraph_steiner_dreyfus_wagner(
igraph_vector_int_remove(&steiner_terminals_copy, 0);

/*
* DP table with size number of vertices in the graph + 2 ^ (number of steiner_terminals_copy) - (number of steiner_terminals_copy + 1)
* 2 ^ (number of steiner_terminals_copy) - (number of steiner_terminals_copy + 1) is number of subsets.
* DP table with size number of vertices in the graph + 2 ^ (number of steiner_terminals_copy) - (number of steiner_terminals_copy + 1)
* 2 ^ (number of steiner_terminals_copy) - (number of steiner_terminals_copy + 1) is number of subsets.
* DP table with size number of vertices in the graph + number of subsets
* Number of subsets is 2 ^ (number of steiner_terminals_copy) - (number of steiner_terminals_copy + 1)
*/

IGRAPH_CHECK(igraph_matrix_init(&dp_cache, no_of_nodes + pow(2, igraph_vector_int_size(&steiner_terminals_copy)) - (igraph_vector_int_size(&steiner_terminals_copy) + 1), no_of_nodes));
IGRAPH_CHECK(
igraph_matrix_init(&dp_cache,
no_of_nodes +
pow(2, igraph_vector_int_size(&steiner_terminals_copy))
- (igraph_vector_int_size(&steiner_terminals_copy) + 1),
no_of_nodes));
IGRAPH_FINALLY(igraph_matrix_destroy, &dp_cache);

std::vector<std::vector<int_set> > distance_matrix = std::vector<std::vector<int_set> >(no_of_nodes + pow(2, igraph_vector_int_size(&steiner_terminals_copy)) - (igraph_vector_int_size(&steiner_terminals_copy) + 1), std::vector<int_set>(no_of_nodes, int_set()));
/* Addition to the dp_cache where at the same indices of the matrix we are storing the set of edge ids that are the shortest path to it
std::vector<std::vector<int_set> > distance_matrix =
std::vector<std::vector<int_set> >
(
no_of_nodes + pow(2, igraph_vector_int_size(&steiner_terminals_copy)) -
(igraph_vector_int_size(&steiner_terminals_copy) + 1),
std::vector<int_set>(no_of_nodes, int_set())
);
/* Addition to the dp_cache where at the same indices of the matrix we are storing
the set of edge ids that are the shortest path to it
*/
igraph_matrix_fill(&dp_cache, IGRAPH_INFINITY);
/*
Expand Down Expand Up @@ -349,7 +372,11 @@ igraph_error_t igraph_steiner_dreyfus_wagner(
* The index would be used in DP table.
*/
dictionary subsetMap;
IGRAPH_CHECK(generateSubsets(&steiner_terminals_copy, igraph_vector_int_size(&steiner_terminals_copy), no_of_nodes, subsetMap, allSubsets));
IGRAPH_CHECK(
generateSubsets(
&steiner_terminals_copy,
igraph_vector_int_size(&steiner_terminals_copy),
no_of_nodes, subsetMap, allSubsets));

int steiner_terminals_copy_size = igraph_vector_int_size(&steiner_terminals_copy);
for (igraph_integer_t m = 2; m <= steiner_terminals_copy_size; m++) {
Expand Down Expand Up @@ -380,15 +407,23 @@ igraph_error_t igraph_steiner_dreyfus_wagner(
igraph_real_t distance1 = IGRAPH_INFINITY;
int_set set_u;
for (auto E : Subsets) {
igraph_integer_t indexOfSubsetE = (E.size() == 1) ? *E.begin() : fetchIndexofMapofSets(E, subsetMap);
igraph_integer_t indexOfSubsetE =
(E.size() == 1)
? *E.begin()
: fetchIndexofMapofSets(E, subsetMap);

igraph_real_t distanceEJ = MATRIX(dp_cache, indexOfSubsetE, j);

int_set DMinusE;

std::set_difference(D.begin(), D.end(), E.begin(), E.end(), std::inserter(DMinusE, DMinusE.end()));
std::set_difference(
D.begin(), D.end(), E.begin(), E.end(),
std::inserter(DMinusE, DMinusE.end()));

igraph_integer_t indexOfSubsetDMinusE = (DMinusE.size() == 1) ? *DMinusE.begin() : fetchIndexofMapofSets(DMinusE, subsetMap);
igraph_integer_t indexOfSubsetDMinusE =
(DMinusE.size() == 1)
? *DMinusE.begin()
: fetchIndexofMapofSets(DMinusE, subsetMap);

if ((distanceEJ + MATRIX(dp_cache, indexOfSubsetDMinusE, j)) < distance1) {
distance1 = distanceEJ + MATRIX(dp_cache, indexOfSubsetDMinusE, j);
Expand All @@ -397,7 +432,9 @@ igraph_error_t igraph_steiner_dreyfus_wagner(
auto& setEJ = distance_matrix[indexOfSubsetE][j];
auto& setDMinusEJ = distance_matrix[indexOfSubsetDMinusE][j];
set_u.clear();
std::set_union(setEJ.begin(), setEJ.end(), setDMinusEJ.begin(), setDMinusEJ.end(), std::inserter(set_u, set_u.end()));
std::set_union(
setEJ.begin(), setEJ.end(), setDMinusEJ.begin(), setDMinusEJ.end(),
std::inserter(set_u, set_u.end()));
}
}

Expand All @@ -408,7 +445,11 @@ igraph_error_t igraph_steiner_dreyfus_wagner(
//get the reference to this set and combine them
auto& setKJ = distance_matrix[k][j];
distance_matrix[indexOfSubsetD][k].clear();
std::set_union(setKJ.begin(), setKJ.end(), set_u.begin(), set_u.end(), std::inserter(distance_matrix[indexOfSubsetD][k], distance_matrix[indexOfSubsetD][k].end()));
std::set_union(
setKJ.begin(), setKJ.end(), set_u.begin(), set_u.end(),
std::inserter(
distance_matrix[indexOfSubsetD][k],
distance_matrix[indexOfSubsetD][k].end()));

}
}
Expand All @@ -427,7 +468,8 @@ igraph_error_t igraph_steiner_dreyfus_wagner(
C_prime.insert(igraph_vector_int_get(&steiner_terminals_copy, i));
}
}
generateD_E(C_prime, E_subsets, C_1); // E are subsets of C such that C[1] is in E and E is subset of C where E != C
// E are subsets of C such that C[1] is in E and E is subset of C where E != C
generateD_E(C_prime, E_subsets, C_1);


igraph_real_t distance2 = IGRAPH_INFINITY;
Expand All @@ -439,12 +481,20 @@ igraph_error_t igraph_steiner_dreyfus_wagner(
int_set set_u;

for (auto E : E_subsets) {
igraph_integer_t indexE = (E.size() == 1) ? *E.begin() : fetchIndexofMapofSets(E, subsetMap);
igraph_integer_t indexE =
(E.size() == 1)
? *E.begin()
: fetchIndexofMapofSets(E, subsetMap);

int_set CMinusE;
std::set_difference(C.begin(), C.end(), E.begin(), E.end(), std::inserter(CMinusE, CMinusE.end()));
std::set_difference(
C.begin(), C.end(), E.begin(), E.end(),
std::inserter(CMinusE, CMinusE.end()));

igraph_integer_t indexC_E = (CMinusE.size() == 1) ? *CMinusE.begin() : fetchIndexofMapofSets(CMinusE, subsetMap);
igraph_integer_t indexC_E =
(CMinusE.size() == 1)
? *CMinusE.begin()
: fetchIndexofMapofSets(CMinusE, subsetMap);

igraph_real_t distanceEJ = MATRIX(dp_cache, indexE, j);
if (((distanceEJ + (MATRIX(dp_cache, indexC_E, j))) < distance1)) {
Expand All @@ -455,7 +505,9 @@ igraph_error_t igraph_steiner_dreyfus_wagner(
set_u.clear();
auto& setEJ = distance_matrix[indexE][j];
auto& setCMinusEJ = distance_matrix[indexC_E][j];
std::set_union(setEJ.begin(), setEJ.end(), setCMinusEJ.begin(), setCMinusEJ.end(), std::inserter(set_u, set_u.end()));
std::set_union(
setEJ.begin(), setEJ.end(), setCMinusEJ.begin(), setCMinusEJ.end(),
std::inserter(set_u, set_u.end()));
}
}

Expand All @@ -464,11 +516,14 @@ igraph_error_t igraph_steiner_dreyfus_wagner(
//get the reference to this set and combine them
final_set.clear();
auto& setQJ = distance_matrix[q][j];
std::set_union(setQJ.begin(), setQJ.end(), set_u.begin(), set_u.end(), std::inserter(final_set, final_set.end()));
std::set_union(
setQJ.begin(), setQJ.end(), set_u.begin(), set_u.end(),
std::inserter(final_set, final_set.end()));
}
}
*res = distance2;
//put the edges in the res_tree and move the final value to res which was stored in distance2 for the scope of this function
//put the edges in the res_tree and move the final value to res,
//which was stored in distance2 for the scope of this function
igraph_vector_int_clear(res_tree);
for (auto elem : final_set) {
igraph_vector_int_push_back(res_tree, elem);
Expand All @@ -486,4 +541,4 @@ igraph_error_t igraph_steiner_dreyfus_wagner(
}
IGRAPH_HANDLE_EXCEPTIONS_END;
return IGRAPH_SUCCESS;
}
}

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