I have an application where for a given fixed number of vertices, there is a need to solve large number of different max-flow algorithms from a given fixed source (S) to a given fixed sink (T). Each max-flow problem differs in that the directed arcs themselves change along with their capacities. As an example, see below.
The number of vertices remains fixed, but the actual arcs and their capacities differ from one problem to the next.
I have the following code that solves the max-flow problem iteratively for Graph 1 and Graph 2 in the figure above using boost thus (apologies for the wall of text, I have tried to make it as minimal as possible. The code below fully compiles on g++ on my linux box, but I am unable to have this correcly compile on online compilers such as wandbox, etc.):
#include <boost/config.hpp>
#include <iostream>
#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/boykov_kolmogorov_max_flow.hpp>
using namespace boost;
typedef adjacency_list_traits<vecS, vecS, directedS> Traits;
typedef adjacency_list<
vecS, vecS, directedS,
property<
vertex_name_t, std::string,
property<vertex_index_t, int,
property<vertex_color_t, boost::default_color_type,
property<vertex_distance_t, double,
property<vertex_predecessor_t, Traits::edge_descriptor>
> > > >,
property<
edge_index_t, int,
property<edge_capacity_t, double,
property<edge_weight_t, double,
property<edge_residual_capacity_t, double,
property<edge_reverse_t, Traits::edge_descriptor>
> > > > >
Graph;
Graph g;
property_map<Graph, edge_index_t>::type e;
property_map<Graph, edge_capacity_t>::type cap;
property_map<Graph, edge_weight_t>::type cost;
property_map<Graph, edge_residual_capacity_t>::type rescap;
property_map<Graph, edge_reverse_t>::type rev;
property_map<Graph, vertex_color_t>::type colors;
void initialize(int nnodes) {
e = get(edge_index, g);
cap = get(edge_capacity, g);
cost = get(edge_weight, g);
rescap = get(edge_residual_capacity, g);
rev = get(edge_reverse, g);
colors = get(vertex_color, g);
for(int i = 0; i < nnodes; i++)
add_vertex(g);
}
void clearedges() {
Graph::vertex_iterator v, vend;
for (boost::tie(v, vend) = vertices(g); v != vend; ++v)
boost::clear_out_edges(*v, g);
}
void createedges(std::vector<std::pair<int, int>>& arcs, std::vector<double>& capacity) {
Traits::edge_descriptor edf, edr;//forward and reverse
for (int eindex = 0, sz = static_cast<int>(arcs.size()); eindex < sz; eindex++) {
int fr, to;
fr = arcs[eindex].first;
to = arcs[eindex].second;
edf = add_edge(fr, to, g).first;
edr = add_edge(to, fr, g).first;
e[edf] = 2 * eindex;
e[edr] = e[edf] + 1;
cap[edf] = capacity[eindex];
cap[edr] = capacity[eindex];
rev[edf] = edr;
rev[edr] = edf;
}
}
double solve_max_flow(int s, int t) {
double retval = boykov_kolmogorov_max_flow(g, s, t);
return retval;
}
bool is_part_of_source(int i) {
if (colors[i] == boost::black_color)
return true;
return false;
}
int main() {
initialize(6);
std::vector<std::pair<int, int>> arcs1 = { std::make_pair<int,int>(0,1),
std::make_pair<int,int>(0,2),
std::make_pair<int,int>(1,2),
std::make_pair<int,int>(1,3),
std::make_pair<int,int>(1,4),
std::make_pair<int,int>(2,4),
std::make_pair<int,int>(3,4),
std::make_pair<int,int>(3,5),
std::make_pair<int,int>(4,5)
};
std::vector<double> capacities1 = { 10, 10, 10, 10, 1, 4, 3, 2, 10 };
clearedges();
createedges(arcs1, capacities1);
double maxflow = solve_max_flow(0, 5);
printf("max flow is %f\n", maxflow);
for (int i = 0; i < 6; i++)
if (is_part_of_source(i))
printf("Node %d belongs to subset source is in\n", i);
Graph::edge_iterator e_, eend_;
int Eindex = 0;
for (boost::tie(e_, eend_) = edges(g); e_ != eend_; ++e_) {
int fr = source(*e_, g);
int to = target(*e_, g);
printf("(%d) Edge %d: (%d -> %d), capacity %f\n", Eindex, e[*e_], fr, to, cap[*e_]);
Eindex++;
if (is_part_of_source(fr) && is_part_of_source(to) == false)
printf("----is part of ST Cut-----\n");
else
printf("x\n");
}
std::vector<std::pair<int, int>> arcs2 = { std::make_pair<int,int>(0,1),
std::make_pair<int,int>(0,2),
std::make_pair<int,int>(1,3),
std::make_pair<int,int>(2,4),
std::make_pair<int,int>(3,5),
std::make_pair<int,int>(4,5)
};
std::vector<double> capacities2 = { 10, 10, 10, 4, 2, 0 };
clearedges();
createedges(arcs2, capacities2);
maxflow = solve_max_flow(0, 5);
printf("max flow is %f\n", maxflow);
for (int i = 0; i < 6; i++)
if (is_part_of_source(i))
printf("Node %d belongs to subset source is in\n", i);
Eindex = 0;
for (boost::tie(e_, eend_) = edges(g); e_ != eend_; ++e_) {
int fr = source(*e_, g);
int to = target(*e_, g);
printf("(%d) Edge %d: (%d -> %d), capacity %f\n", Eindex, e[*e_], fr, to, cap[*e_]);
Eindex++;
if (is_part_of_source(fr) && is_part_of_source(to) == false)
printf("----is part of ST Cut-----\n");
else
printf("x\n");
}
getchar();
}
I have the following questions.
(a) If the underlying vertices remain fixed, but only the arcs and their capacities change from iteration to iteration, is there anything faster than using clear_out_edges to clear the arcs and then using add_edge to add the new arcs with their new capacities? Also, does clear_out_edges correctly also clear the property map entries that may have the edge descriptor just deleted as key?
(b) Boost max-flow algorithms seem to want the explicit addition of reverse arcs. As of now, in function createedges I explicitly do this via a forward edge descriptor (edf) and a reverse edge descriptor (edr). Is there any performance penalty for this especially when the number of max flow problems that need to be solved is in the 1000s? Is there anything that is more efficient than this?
(c) I am able to correctly enumerate the arcs of the minimal S/T cut via the following portion of the code:
int Eindex = 0;
for (boost::tie(e_, eend_) = edges(g); e_ != eend_; ++e_) {
int fr = source(*e_, g);
int to = target(*e_, g);
printf("(%d) Edge %d: (%d -> %d), capacity %f\n", Eindex, e[*e_], fr, to, cap[*e_]);
Eindex++;
if (is_part_of_source(fr) && is_part_of_source(to) == false)
printf("----is part of ST Cut-----\n");
else
printf("x\n");
}
Is there any more efficient way or enumerating the arcs of the S/T cut than the above?
There's many issues. If you use modern C++ and compiler warnings, you can reduce the code and spot the bugs in printing vertex descriptors (printf is just not safe; use the diagnostics!).
Here's my take after review.
Notable changes:
bundled properties instead of separate interior properties
this implies passing named arguments (but see https://stackoverflow.com/a/64744086/85371)
no more global variables, no more loopy initialization if the simple constructor suffices
no more duplicated code (nothing invites error quite like having capacities1 and capacities2 lying around)
using clear_vertex instead of just clear_out_edges - this may not make a difference (?) but seems to express intent a bit better
no more printf (I'll use libfmt, which is also in c++23), so e.g.
fmt::print("Max flow {}\nNodes {} are in source subset\n", maxflow,
vertices(_g) | filtered(is_source));
prints
Max flow 10
Nodes {0, 1, 2, 3} are in source subset
all in one go
print what you think you are printing. In particular, use the library support for printing edges if you can
Live On Compiler Explorer
#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/boykov_kolmogorov_max_flow.hpp>
#include <boost/range/adaptors.hpp>
#include <fmt/ostream.h>
#include <fmt/ranges.h>
using boost::adaptors::filtered;
using Traits = boost::adjacency_list_traits<boost::vecS, boost::vecS, boost::directedS>;
using V = Traits::vertex_descriptor;
using E = Traits::edge_descriptor;
using Capacity = double;
using Color = boost::default_color_type;
struct VertexProps {
// std::string name;
Color color;
Capacity distance;
E predecessor;
};
struct EdgeProps {
int id;
Capacity weight, residual;
E reverse;
};
using Graph = boost::adjacency_list<
boost::vecS, boost::vecS, boost::directedS,
VertexProps,
// see https://stackoverflow.com/a/64744086/85371 :(
boost::property<boost::edge_capacity_t, Capacity, EdgeProps>>;
struct MyGraph {
MyGraph(size_t nnodes) : _g(nnodes) {}
void runSimulation(auto const& arcs, auto const& capacities)
{
reconfigure(arcs, capacities);
Capacity maxflow = solve_max_flow(0, 5);
auto cap = get(boost::edge_capacity, _g);
auto is_source = [this](V v) { return _g[v].color == Color::black_color; };
fmt::print("Max flow {}\nNodes {} are in source subset\n", maxflow,
vertices(_g) | filtered(is_source));
for (E e : boost::make_iterator_range(edges(_g))) {
bool st_cut =
is_source(source(e, _g)) and
not is_source(target(e, _g));
fmt::print("Edge {} (id #{:2}), capacity {:3} {}\n", e, _g[e].id,
cap[e], st_cut ? "(ST Cut)" : "");
}
}
private:
Graph _g;
void reconfigure(auto const& arcs, auto const& capacities)
{
assert(arcs.size() == capacities.size());
for (auto v : boost::make_iterator_range(vertices(_g))) {
// boost::clear_out_edges(v, g);
boost::clear_vertex(v, _g);
}
auto cap = get(boost::edge_capacity, _g);
auto eidx = get(&EdgeProps::id, _g);
auto rev = get(&EdgeProps::reverse, _g);
auto eindex = 0;
for (auto [fr, to] : arcs) {
auto edf = add_edge(fr, to, _g).first;
auto edr = add_edge(to, fr, _g).first;
eidx[edf] = 2 * eindex;
eidx[edr] = eidx[edf] + 1;
cap[edf] = cap[edr] = capacities[eindex];
rev[edf] = edr;
rev[edr] = edf;
++eindex;
}
}
Capacity solve_max_flow(V src, V sink)
{
return boykov_kolmogorov_max_flow(
_g, src, sink,
// named arguments
boost::reverse_edge_map(get(&EdgeProps::reverse, _g))
.residual_capacity_map(get(&EdgeProps::residual, _g))
.vertex_color_map(get(&VertexProps::color, _g))
.predecessor_map(get(&VertexProps::predecessor, _g))
.distance_map(get(&VertexProps::distance, _g))
// end named arguments
);
}
};
int main() {
MyGraph g{6};
using namespace std;
for (auto&& [arcs, capacities] : { tuple
// 1
{vector{pair{0, 1}, {0, 2}, {1, 2}, {1, 3}, {1, 4},
{2, 4}, {3, 4}, {3, 5}, {4, 5}},
vector{10, 10, 10, 10, 1, 4, 3, 2, 10}},
// 2
{vector{pair{0, 1}, {0, 2}, {1, 3}, {2, 4}, {3, 5}, {4, 5}},
vector{10, 10, 10, 4, 2, 0}},
})
{
g.runSimulation(arcs, capacities);
}
}
Prints
Max flow 10
Nodes {0, 1, 2, 3} are in source subset
Edge (0,1) (id # 0), capacity 10
Edge (0,2) (id # 2), capacity 10
Edge (1,0) (id # 1), capacity 10
Edge (1,2) (id # 4), capacity 10
Edge (1,3) (id # 6), capacity 10
Edge (1,4) (id # 8), capacity 1 (ST Cut)
Edge (2,0) (id # 3), capacity 10
Edge (2,1) (id # 5), capacity 10
Edge (2,4) (id #10), capacity 4 (ST Cut)
Edge (3,1) (id # 7), capacity 10
Edge (3,4) (id #12), capacity 3 (ST Cut)
Edge (3,5) (id #14), capacity 2 (ST Cut)
Edge (4,1) (id # 9), capacity 1
Edge (4,2) (id #11), capacity 4
Edge (4,3) (id #13), capacity 3
Edge (4,5) (id #16), capacity 10
Edge (5,3) (id #15), capacity 2
Edge (5,4) (id #17), capacity 10
Max flow 2
Nodes {0, 1, 2, 3, 4} are in source subset
Edge (0,1) (id # 0), capacity 10
Edge (0,2) (id # 2), capacity 10
Edge (1,0) (id # 1), capacity 10
Edge (1,3) (id # 4), capacity 10
Edge (2,0) (id # 3), capacity 10
Edge (2,4) (id # 6), capacity 4
Edge (3,1) (id # 5), capacity 10
Edge (3,5) (id # 8), capacity 2 (ST Cut)
Edge (4,2) (id # 7), capacity 4
Edge (4,5) (id #10), capacity 0 (ST Cut)
Edge (5,3) (id # 9), capacity 2
Edge (5,4) (id #11), capacity 0
Side Note
If you think main is overcomplicated, here's another way to write it for just the two invocations:
Live On Compiler Explorer
g.runSimulation({{0, 1}, {0, 2}, {1, 2}, {1, 3}, {1, 4}, {2, 4}, {3, 4}, {3, 5}, {4, 5}},
{10, 10, 10, 10, 1, 4, 3, 2, 10});
g.runSimulation({{0, 1}, {0, 2}, {1, 3}, {2, 4}, {3, 5}, {4, 5}},
{10, 10, 10, 4, 2, 0});
Currently self-learning C++ with Daniel Liang's Introduction to C++.
On the topic of the merge sort, I cannot seem to understand how his code is recursively calling itself.
I understand the general concept of the merge sort, but I am having trouble understanding this code specifically.
In this example, we first pass the list 1, 7, 3, 4, 9, 3, 3, 1, 2, and its size (9) to the mergeSort function.
From there, we divide the list into two until the array size reaches 1. In this case, we would get: 1,7,3,4 -> 1,7 -> 1. We then move onto the merge sorting the second half. The second half array would be 7 in this case. We merge the two arrays [1] and [7] and proceed to delete the two arrays that were dynamically allocated to prevent any memory leak.
The part I don't understand is how does this code run from here? After delete[] firstHalf and delete[] secondHalf. From my understanding, shouldn't there be another mergeSort function call in order to merge sort the new firstHalf and secondHalf?
#include <iostream>
using namespace std;
// Function prototype
void arraycopy(int source[], int sourceStartIndex,
int target[], int targetStartIndex, int length);
void merge(int list1[], int list1Size,
int list2[], int list2Size, int temp[]);
// The function for sorting the numbers
void mergeSort(int list[], int arraySize)
{
if (arraySize > 1)
{
// Merge sort the first half
int* firstHalf = new int[arraySize / 2];
arraycopy(list, 0, firstHalf, 0, arraySize / 2);
mergeSort(firstHalf, arraySize / 2);
// Merge sort the second half
int secondHalfLength = arraySize - arraySize / 2;
int* secondHalf = new int[secondHalfLength];
arraycopy(list, arraySize / 2, secondHalf, 0, secondHalfLength);
mergeSort(secondHalf, secondHalfLength);
// Merge firstHalf with secondHalf
merge(firstHalf, arraySize / 2, secondHalf, secondHalfLength,
list);
delete [] firstHalf;
delete [] secondHalf;
}
}
void merge(int list1[], int list1Size,
int list2[], int list2Size, int temp[])
{
int current1 = 0; // Current index in list1
int current2 = 0; // Current index in list2
int current3 = 0; // Current index in temp
while (current1 < list1Size && current2 < list2Size)
{
if (list1[current1] < list2[current2])
temp[current3++] = list1[current1++];
else
temp[current3++] = list2[current2++];
}
while (current1 < list1Size)
temp[current3++] = list1[current1++];
while (current2 < list2Size)
temp[current3++] = list2[current2++];
}
void arraycopy(int source[], int sourceStartIndex,
int target[], int targetStartIndex, int length)
{
for (int i = 0; i < length; i++)
{
target[i + targetStartIndex] = source[i + sourceStartIndex];
}
}
int main()
{
const int SIZE = 9;
int list[] = {1, 7, 3, 4, 9, 3, 3, 1, 2};
mergeSort(list, SIZE);
for (int i = 0; i < SIZE; i++)
cout << list[i] << " ";
return 0;
}
From my understanding, shouldn't there be another mergeSort function
call in order to merge sort the new firstHalf and secondHalf?
It is happening implicitly during the recursive call. When you reach these two lines:
delete [] firstHalf;
delete [] secondHalf;
It means that one call to mergeSort is completed. If this call belongs to merging a first half, then code starts from the line after, i.e. these lines:
// Merge sort the second half
int secondHalfLength = arraySize - arraySize / 2;
...
But, if this call belongs to merging of the second half, then the control goes back to the line just after that call, i.e. these lines:
// Merge firstHalf with secondHalf
merge(firstHalf, arraySize / 2, secondHalf, secondHalfLength,
list);
And everything if doing well as planned.
I need a class iterator like this
https://github.com/thrust/thrust/blob/master/examples/strided_range.cu
but that this new iterator do the next sequence
[k * size_stride, k * size_stride+1, ...,k * size_stride+size_chunk-1,...]
with
k = 0,1,...,N
Example:
size_stride = 8
size_chunk = 3
N = 3
then the sequence is
[0,1,2,8,9,10,16,17,18,24,25,26]
I don't know how do this efficiently...
The strided range interator is basically a carefully crafted permutation iterator with a functor that gives the appropriate indices for permutation.
Here is a modification to the strided range iterator example. The main changes were:
include the chunk size as an iterator parameter
modify the functor that provides the indices for the permutation iterator to spit out the desired sequence
adjust the definitions of .end() iterator to provide the appropriate length of sequence.
Worked example:
$ cat t1280.cu
#include <thrust/iterator/counting_iterator.h>
#include <thrust/iterator/transform_iterator.h>
#include <thrust/iterator/permutation_iterator.h>
#include <thrust/functional.h>
#include <thrust/fill.h>
#include <thrust/device_vector.h>
#include <thrust/copy.h>
#include <thrust/sequence.h>
#include <iostream>
#include <assert.h>
// this example illustrates how to make strided-chunk access to a range of values
// examples:
// strided_chunk_range([0, 1, 2, 3, 4, 5, 6], 1,1) -> [0, 1, 2, 3, 4, 5, 6]
// strided_chunk_range([0, 1, 2, 3, 4, 5, 6], 2,1) -> [0, 2, 4, 6]
// strided_chunk_range([0, 1, 2, 3, 4, 5, 6], 3,2) -> [0 ,1, 3, 4, 6]
// ...
template <typename Iterator>
class strided_chunk_range
{
public:
typedef typename thrust::iterator_difference<Iterator>::type difference_type;
struct stride_functor : public thrust::unary_function<difference_type,difference_type>
{
difference_type stride;
int chunk;
stride_functor(difference_type stride, int chunk)
: stride(stride), chunk(chunk) {}
__host__ __device__
difference_type operator()(const difference_type& i) const
{
int pos = i/chunk;
return ((pos * stride) + (i-(pos*chunk)));
}
};
typedef typename thrust::counting_iterator<difference_type> CountingIterator;
typedef typename thrust::transform_iterator<stride_functor, CountingIterator> TransformIterator;
typedef typename thrust::permutation_iterator<Iterator,TransformIterator> PermutationIterator;
// type of the strided_range iterator
typedef PermutationIterator iterator;
// construct strided_range for the range [first,last)
strided_chunk_range(Iterator first, Iterator last, difference_type stride, int chunk)
: first(first), last(last), stride(stride), chunk(chunk) {assert(chunk<=stride);}
iterator begin(void) const
{
return PermutationIterator(first, TransformIterator(CountingIterator(0), stride_functor(stride, chunk)));
}
iterator end(void) const
{
int lmf = last-first;
int nfs = lmf/stride;
int rem = lmf-(nfs*stride);
return begin() + (nfs*chunk) + ((rem<chunk)?rem:chunk);
}
protected:
Iterator first;
Iterator last;
difference_type stride;
int chunk;
};
int main(void)
{
thrust::device_vector<int> data(50);
thrust::sequence(data.begin(), data.end());
typedef thrust::device_vector<int>::iterator Iterator;
// create strided_chunk_range
std::cout << "stride 3, chunk 2, length 7" << std::endl;
strided_chunk_range<Iterator> scr1(data.begin(), data.begin()+7, 3, 2);
thrust::copy(scr1.begin(), scr1.end(), std::ostream_iterator<int>(std::cout, " ")); std::cout << std::endl;
std::cout << "stride 8, chunk 3, length 50" << std::endl;
strided_chunk_range<Iterator> scr(data.begin(), data.end(), 8, 3);
thrust::copy(scr.begin(), scr.end(), std::ostream_iterator<int>(std::cout, " ")); std::cout << std::endl;
return 0;
}
$ nvcc -arch=sm_35 -o t1280 t1280.cu
$ ./t1280
stride 3, chunk 2, length 7
0 1 3 4 6
stride 8, chunk 3, length 50
0 1 2 8 9 10 16 17 18 24 25 26 32 33 34 40 41 42 48 49
$
This is probably not the most optimal implementation, in particular because we are doing division in the permutation functor, but it should get you started.
I assume (and test for) chunk<=stride, because this seemed reasonable to me, and simplified my thought process. I'm sure it could be modified, with an appropriate example of what sequence you would like to see, for the case where chunk>stride.