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gtsam/gtsam_unstable/partition/FindSeparator-inl.h

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/*
* FindSeparator-inl.h
*
* Created on: Nov 23, 2010
* Updated: Feb 20. 2014
* Author: nikai
* Author: Andrew Melim
* Description: find the separator of bisectioning for a given graph
*/
#pragma once
#include <stdexcept>
#include <iostream>
#include <vector>
#include <optional>
#include <boost/shared_array.hpp>
#include <gtsam/base/timing.h>
#include "FindSeparator.h"
#include <metis.h>
extern "C" {
#include <metislib.h>
}
namespace gtsam { namespace partition {
typedef boost::shared_array<idx_t> sharedInts;
/* ************************************************************************* */
/**
* Return the size of the separator and the partiion indices {part}
* Part [j] is 0, 1, or 2, depending on
* whether node j is in the left part of the graph, the right part, or the
* separator, respectively
*/
std::pair<int, sharedInts> separatorMetis(idx_t n, const sharedInts& xadj,
const sharedInts& adjncy, const sharedInts& adjwgt, bool verbose) {
// control parameters
std::vector<idx_t> vwgt; // the weights of the vertices
idx_t options[METIS_NOPTIONS];
METIS_SetDefaultOptions(options); // use defaults
idx_t sepsize; // the size of the separator, output
sharedInts part_(new idx_t[n]); // the partition of each vertex, output
// set uniform weights on the vertices
vwgt.assign(n, 1);
// TODO: Fix at later time
//boost::timer::cpu_timer TOTALTmr;
if (verbose) {
printf("**********************************************************************\n");
printf("Graph Information ---------------------------------------------------\n");
printf(" #Vertices: %d, #Edges: %u\n", n, *(xadj.get()+n) / 2);
printf("\nND Partitioning... -------------------------------------------\n");
//TOTALTmr.start()
}
// call metis parition routine
METIS_ComputeVertexSeparator(&n, xadj.get(), adjncy.get(),
&vwgt[0], options, &sepsize, part_.get());
if (verbose) {
//boost::cpu_times const elapsed_times(timer.elapsed());
//printf("\nTiming Information --------------------------------------------------\n");
//printf(" Total: \t\t %7.3f\n", elapsed_times);
printf(" Sep size: \t\t %d\n", sepsize);
printf("**********************************************************************\n");
}
return std::make_pair(sepsize, part_);
}
/* ************************************************************************* */
void modefied_EdgeComputeSeparator(idx_t *nvtxs, idx_t *xadj, idx_t *adjncy, idx_t *vwgt,
idx_t *adjwgt, idx_t *options, idx_t *edgecut, idx_t *part)
{
idx_t i, ncon;
graph_t *graph;
real_t *tpwgts2;
ctrl_t *ctrl;
ctrl = SetupCtrl(METIS_OP_OMETIS, options, 1, 3, nullptr, nullptr);
ctrl->iptype = METIS_IPTYPE_GROW;
//if () == nullptr)
// return METIS_ERROR_INPUT;
InitRandom(ctrl->seed);
graph = SetupGraph(ctrl, *nvtxs, 1, xadj, adjncy, vwgt, nullptr, nullptr);
AllocateWorkSpace(ctrl, graph);
ncon = graph->ncon;
ctrl->ncuts = 1;
/* determine the weights of the two partitions as a function of the weight of the
target partition weights */
tpwgts2 = rwspacemalloc(ctrl, 2*ncon);
for (i=0; i<ncon; i++) {
tpwgts2[i] = rsum((2>>1), ctrl->tpwgts+i, ncon);
tpwgts2[ncon+i] = 1.0 - tpwgts2[i];
}
/* perform the bisection */
*edgecut = MultilevelBisect(ctrl, graph, tpwgts2);
// ConstructMinCoverSeparator(&ctrl, &graph, 1.05);
// *edgecut = graph->mincut;
// *sepsize = graph.pwgts[2];
icopy(*nvtxs, graph->where, part);
std::cout << "Finished bisection:" << *edgecut << std::endl;
FreeGraph(&graph);
FreeCtrl(&ctrl);
}
/* ************************************************************************* */
/**
* Return the number of edge cuts and the partition indices {part}
* Part [j] is 0 or 1, depending on
* whether node j is in the left part of the graph or the right part respectively
*/
std::pair<int, sharedInts> edgeMetis(idx_t n, const sharedInts& xadj, const sharedInts& adjncy,
const sharedInts& adjwgt, bool verbose) {
// control parameters
std::vector<idx_t> vwgt; // the weights of the vertices
idx_t options[METIS_NOPTIONS];
METIS_SetDefaultOptions(options); // use defaults
idx_t edgecut; // the number of edge cuts, output
sharedInts part_(new idx_t[n]); // the partition of each vertex, output
// set uniform weights on the vertices
vwgt.assign(n, 1);
//TODO: Fix later
//boost::timer TOTALTmr;
if (verbose) {
printf("**********************************************************************\n");
printf("Graph Information ---------------------------------------------------\n");
printf(" #Vertices: %d, #Edges: %u\n", n, *(xadj.get()+n) / 2);
printf("\nND Partitioning... -------------------------------------------\n");
//cleartimer(TOTALTmr);
//starttimer(TOTALTmr);
}
//int wgtflag = 1; // only edge weights
//int numflag = 0; // c style numbering starting from 0
//int nparts = 2; // partition the graph to 2 submaps
modefied_EdgeComputeSeparator(&n, xadj.get(), adjncy.get(), &vwgt[0], adjwgt.get(),
options, &edgecut, part_.get());
if (verbose) {
//stoptimer(TOTALTmr);
printf("\nTiming Information --------------------------------------------------\n");
//printf(" Total: \t\t %7.3f\n", gettimer(TOTALTmr));
printf(" Edge cuts: \t\t %d\n", edgecut);
printf("**********************************************************************\n");
}
return std::make_pair(edgecut, part_);
}
/* ************************************************************************* */
/**
* Prepare the data structure {xadj} and {adjncy} required by metis
* xadj always has the size equal to the no. of the nodes plus 1
* adjncy always has the size equal to two times of the no. of the edges in the Metis graph
*/
template <class GenericGraph>
void prepareMetisGraph(const GenericGraph& graph, const std::vector<size_t>& keys, WorkSpace& workspace,
sharedInts* ptr_xadj, sharedInts* ptr_adjncy, sharedInts* ptr_adjwgt) {
typedef std::vector<int> Weights;
typedef std::vector<int> Neighbors;
typedef std::pair<Neighbors, Weights> NeighborsInfo;
// set up dictionary
std::vector<int>& dictionary = workspace.dictionary;
workspace.prepareDictionary(keys);
// prepare for {adjacencyMap}, a pair of neighbor indices and the correponding edge weights
int numNodes = keys.size();
int numEdges = 0;
std::vector<NeighborsInfo> adjacencyMap;
adjacencyMap.resize(numNodes);
std::cout << "Number of nodes: " << adjacencyMap.size() << std::endl;
int index1, index2;
for(const typename GenericGraph::value_type& factor: graph){
index1 = dictionary[factor->key1.index];
index2 = dictionary[factor->key2.index];
std::cout << "index1: " << index1 << std::endl;
std::cout << "index2: " << index2 << std::endl;
// if both nodes are in the current graph, i.e. not a joint factor between frontal and separator
if (index1 >= 0 && index2 >= 0) {
std::pair<Neighbors, Weights>& adjacencyMap1 = adjacencyMap[index1];
std::pair<Neighbors, Weights>& adjacencyMap2 = adjacencyMap[index2];
try{
adjacencyMap1.first.push_back(index2);
adjacencyMap1.second.push_back(factor->weight);
adjacencyMap2.first.push_back(index1);
adjacencyMap2.second.push_back(factor->weight);
}catch(std::exception& e){
std::cout << e.what() << std::endl;
}
numEdges++;
}
}
// prepare for {xadj}, {adjncy}, and {adjwgt}
*ptr_xadj = sharedInts(new idx_t[numNodes+1]);
*ptr_adjncy = sharedInts(new idx_t[numEdges*2]);
*ptr_adjwgt = sharedInts(new idx_t[numEdges*2]);
sharedInts& xadj = *ptr_xadj;
sharedInts& adjncy = *ptr_adjncy;
sharedInts& adjwgt = *ptr_adjwgt;
int ind_xadj = 0, ind_adjncy = 0;
for(const NeighborsInfo& info: adjacencyMap) {
*(xadj.get() + ind_xadj) = ind_adjncy;
std::copy(info.first .begin(), info.first .end(), adjncy.get() + ind_adjncy);
std::copy(info.second.begin(), info.second.end(), adjwgt.get() + ind_adjncy);
assert(info.first.size() == info.second.size());
ind_adjncy += info.first.size();
ind_xadj ++;
}
if (ind_xadj != numNodes) throw std::runtime_error("prepareMetisGraph_: ind_xadj != numNodes");
*(xadj.get() + ind_xadj) = ind_adjncy;
}
/* ************************************************************************* */
template<class GenericGraph>
std::optional<MetisResult> separatorPartitionByMetis(const GenericGraph& graph,
const std::vector<size_t>& keys, WorkSpace& workspace, bool verbose) {
// create a metis graph
size_t numKeys = keys.size();
if (verbose)
std::cout << graph.size() << " factors,\t" << numKeys << " nodes;\t" << std::endl;
sharedInts xadj, adjncy, adjwgt;
prepareMetisGraph<GenericGraph>(graph, keys, workspace, &xadj, &adjncy, &adjwgt);
// run ND on the graph
const auto [sepsize, part] = separatorMetis(numKeys, xadj, adjncy, adjwgt, verbose);
if (!sepsize) return std::optional<MetisResult>();
// convert the 0-1-2 from Metis to 1-2-0, so that the separator is 0, as later
// we will have more submaps
MetisResult result;
result.C.reserve(sepsize);
result.A.reserve(numKeys - sepsize);
result.B.reserve(numKeys - sepsize);
int* ptr_part = part.get();
std::vector<size_t>::const_iterator itKey = keys.begin();
std::vector<size_t>::const_iterator itKeyLast = keys.end();
while(itKey != itKeyLast) {
switch(*(ptr_part++)) {
case 0: result.A.push_back(*(itKey++)); break;
case 1: result.B.push_back(*(itKey++)); break;
case 2: result.C.push_back(*(itKey++)); break;
default: throw std::runtime_error("separatorPartitionByMetis: invalid results from Metis ND!");
}
}
if (verbose) {
std::cout << "total key: " << keys.size()
<< " result(A,B,C) = " << result.A.size() << ", " << result.B.size() << ", "
<< result.C.size() << "; sepsize from Metis = " << sepsize << std::endl;
//throw runtime_error("separatorPartitionByMetis:stop for debug");
}
if(result.C.size() != sepsize) {
std::cout << "total key: " << keys.size()
<< " result(A,B,C) = " << result.A.size() << ", " << result.B.size() << ", " << result.C.size()
<< "; sepsize from Metis = " << sepsize << std::endl;
throw std::runtime_error("separatorPartitionByMetis: invalid sepsize from Metis ND!");
}
return result;
}
/* *************************************************************************/
template<class GenericGraph>
std::optional<MetisResult> edgePartitionByMetis(const GenericGraph& graph,
const std::vector<size_t>& keys, WorkSpace& workspace, bool verbose) {
// a small hack for handling the camera1-camera2 case used in the unit tests
if (graph.size() == 1 && keys.size() == 2) {
MetisResult result;
result.A.push_back(keys.front());
result.B.push_back(keys.back());
return result;
}
// create a metis graph
size_t numKeys = keys.size();
if (verbose) std::cout << graph.size() << " factors,\t" << numKeys << " nodes;\t" << std::endl;
sharedInts xadj, adjncy, adjwgt;
prepareMetisGraph<GenericGraph>(graph, keys, workspace, &xadj, &adjncy, &adjwgt);
// run metis on the graph
const auto [edgecut, part] = edgeMetis(numKeys, xadj, adjncy, adjwgt, verbose);
// convert the 0-1-2 from Metis to 1-2-0, so that the separator is 0, as later we will have more submaps
MetisResult result;
result.A.reserve(numKeys);
result.B.reserve(numKeys);
int* ptr_part = part.get();
std::vector<size_t>::const_iterator itKey = keys.begin();
std::vector<size_t>::const_iterator itKeyLast = keys.end();
while(itKey != itKeyLast) {
if (*ptr_part != 0 && *ptr_part != 1)
std::cout << *ptr_part << "!!!" << std::endl;
switch(*(ptr_part++)) {
case 0: result.A.push_back(*(itKey++)); break;
case 1: result.B.push_back(*(itKey++)); break;
default: throw std::runtime_error("edgePartitionByMetis: invalid results from Metis ND!");
}
}
if (verbose) {
std::cout << "the size of two submaps in the reduced graph: " << result.A.size()
<< " " << result.B.size() << std::endl;
int edgeCut = 0;
for(const typename GenericGraph::value_type& factor: graph){
int key1 = factor->key1.index;
int key2 = factor->key2.index;
// print keys and their subgraph assignment
std::cout << key1;
if (std::find(result.A.begin(), result.A.end(), key1) != result.A.end()) std::cout <<"A ";
if (std::find(result.B.begin(), result.B.end(), key1) != result.B.end()) std::cout <<"B ";
std::cout << key2;
if (std::find(result.A.begin(), result.A.end(), key2) != result.A.end()) std::cout <<"A ";
if (std::find(result.B.begin(), result.B.end(), key2) != result.B.end()) std::cout <<"B ";
std::cout << "weight " << factor->weight;;
// find vertices that were assigned to sets A & B. Their edge will be cut
if ((std::find(result.A.begin(), result.A.end(), key1) != result.A.end() &&
std::find(result.B.begin(), result.B.end(), key2) != result.B.end()) ||
(std::find(result.B.begin(), result.B.end(), key1) != result.B.end() &&
std::find(result.A.begin(), result.A.end(), key2) != result.A.end())){
edgeCut ++;
std::cout << " CUT ";
}
std::cout << std::endl;
}
std::cout << "edgeCut: " << edgeCut << std::endl;
}
return result;
}
/* ************************************************************************* */
bool isLargerIsland(const std::vector<size_t>& island1, const std::vector<size_t>& island2) {
return island1.size() > island2.size();
}
/* ************************************************************************* */
// debug functions
void printIsland(const std::vector<size_t>& island) {
std::cout << "island: ";
for(const size_t key: island)
std::cout << key << " ";
std::cout << std::endl;
}
void printIslands(const std::list<std::vector<size_t> >& islands) {
for(const std::vector<std::size_t>& island: islands)
printIsland(island);
}
void printNumCamerasLandmarks(const std::vector<size_t>& keys, const std::vector<Symbol>& int2symbol) {
int numCamera = 0, numLandmark = 0;
for(const size_t key: keys)
if (int2symbol[key].chr() == 'x')
numCamera++;
else
numLandmark++;
std::cout << "numCamera: " << numCamera << " numLandmark: " << numLandmark << std::endl;
}
/* ************************************************************************* */
template<class GenericGraph>
void addLandmarkToPartitionResult(const GenericGraph& graph, const std::vector<size_t>& landmarkKeys,
MetisResult& partitionResult, WorkSpace& workspace) {
// set up cameras in the dictionary
std::vector<size_t>& A = partitionResult.A;
std::vector<size_t>& B = partitionResult.B;
std::vector<size_t>& C = partitionResult.C;
std::vector<int>& dictionary = workspace.dictionary;
std::fill(dictionary.begin(), dictionary.end(), -1);
for(const size_t a: A)
dictionary[a] = 1;
for(const size_t b: B)
dictionary[b] = 2;
if (!C.empty())
throw std::runtime_error("addLandmarkToPartitionResult: C is not empty");
// set up landmarks
size_t i,j;
for(const typename GenericGraph::value_type& factor: graph) {
i = factor->key1.index;
j = factor->key2.index;
if (dictionary[j] == 0) // if the landmark is already in the separator, continue
continue;
else if (dictionary[j] == -1)
dictionary[j] = dictionary[i];
else {
if (dictionary[j] != dictionary[i])
dictionary[j] = 0;
}
// if (j == 67980)
// std::cout << "dictionary[67980]" << dictionary[j] << std::endl;
}
for(const size_t j: landmarkKeys) {
switch(dictionary[j]) {
case 0: C.push_back(j); break;
case 1: A.push_back(j); break;
case 2: B.push_back(j); break;
default: std::cout << j << ": " << dictionary[j] << std::endl;
throw std::runtime_error("addLandmarkToPartitionResult: wrong status for landmark");
}
}
}
#define REDUCE_CAMERA_GRAPH
/* ************************************************************************* */
template<class GenericGraph>
std::optional<MetisResult> findPartitoning(const GenericGraph& graph, const std::vector<size_t>& keys,
WorkSpace& workspace, bool verbose,
const std::optional<std::vector<Symbol> >& int2symbol, const bool reduceGraph) {
std::optional<MetisResult> result;
GenericGraph reducedGraph;
std::vector<size_t> keyToPartition;
std::vector<size_t> cameraKeys, landmarkKeys;
if (reduceGraph) {
if (!int2symbol.has_value())
throw std::invalid_argument("findSeparator: int2symbol must be valid!");
// find out all the landmark keys, which are to be eliminated
cameraKeys.reserve(keys.size());
landmarkKeys.reserve(keys.size());
for(const size_t key: keys) {
if((*int2symbol)[key].chr() == 'x')
cameraKeys.push_back(key);
else
landmarkKeys.push_back(key);
}
keyToPartition = cameraKeys;
workspace.prepareDictionary(keyToPartition);
const std::vector<int>& dictionary = workspace.dictionary;
reduceGenericGraph(graph, cameraKeys, landmarkKeys, dictionary, reducedGraph);
std::cout << "original graph: V" << keys.size() << ", E" << graph.size()
<< " --> reduced graph: V" << cameraKeys.size() << ", E" << reducedGraph.size() << std::endl;
result = edgePartitionByMetis(reducedGraph, keyToPartition, workspace, verbose);
} else // call Metis to partition the graph to A, B, C
result = separatorPartitionByMetis(graph, keys, workspace, verbose);
if (!result.has_value()) {
std::cout << "metis failed!" << std::endl;
return {};
}
if (reduceGraph) {
addLandmarkToPartitionResult(graph, landmarkKeys, *result, workspace);
std::cout << "the separator size: " << result->C.size() << " landmarks" << std::endl;
}
return result;
}
/* ************************************************************************* */
template<class GenericGraph>
int findSeparator(const GenericGraph& graph, const std::vector<size_t>& keys,
const int minNodesPerMap, WorkSpace& workspace, bool verbose,
const std::optional<std::vector<Symbol> >& int2symbol, const bool reduceGraph,
const int minNrConstraintsPerCamera, const int minNrConstraintsPerLandmark) {
std::optional<MetisResult> result = findPartitoning(graph, keys, workspace,
verbose, int2symbol, reduceGraph);
// find the island in A and B, and make them separated submaps
typedef std::vector<size_t> Island;
std::list<Island> islands;
std::list<Island> islands_in_A = findIslands(graph, result->A, workspace,
minNrConstraintsPerCamera, minNrConstraintsPerLandmark);
std::list<Island> islands_in_B = findIslands(graph, result->B, workspace,
minNrConstraintsPerCamera, minNrConstraintsPerLandmark);
islands.insert(islands.end(), islands_in_A.begin(), islands_in_A.end());
islands.insert(islands.end(), islands_in_B.begin(), islands_in_B.end());
islands.sort(isLargerIsland);
size_t numIsland0 = islands.size();
#ifdef NDEBUG
// verbose = true;
// if (!int2symbol) throw std::invalid_argument("findSeparator: int2symbol is not set!");
// std::cout << "sep size: " << result->C.size() << "; ";
// printNumCamerasLandmarks(result->C, *int2symbol);
// std::cout << "no. of island: " << islands.size() << "; ";
// std::cout << "island size: ";
// for(const Island& island: islands)
// std::cout << island.size() << " ";
// std::cout << std::endl;
// for(const Island& island: islands) {
// printNumCamerasLandmarks(island, int2symbol);
// }
#endif
// absorb small components into the separator
size_t oldSize = islands.size();
while(true) {
if (islands.size() < 2) {
std::cout << "numIsland: " << numIsland0 << std::endl;
throw std::runtime_error("findSeparator: found fewer than 2 submaps!");
}
std::list<Island>::reference island = islands.back();
if ((int)island.size() >= minNodesPerMap) break;
result->C.insert(result->C.end(), island.begin(), island.end());
islands.pop_back();
}
if (islands.size() != oldSize){
if (verbose) std::cout << oldSize << "-" << oldSize - islands.size() << " submap(s);\t" << std::endl;
}
else{
if (verbose) std::cout << oldSize << " submap(s);\t" << std::endl;
}
// generate the node map
std::vector<int>& partitionTable = workspace.partitionTable;
std::fill(partitionTable.begin(), partitionTable.end(), -1);
for(const size_t key: result->C)
partitionTable[key] = 0;
int idx = 0;
for(const Island& island: islands) {
idx++;
for(const size_t key: island) {
partitionTable[key] = idx;
}
}
return islands.size();
}
}} //namespace
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