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verilator/src/V3TSP.cpp

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// -*- mode: C++; c-file-style: "cc-mode" -*-
//*************************************************************************
// DESCRIPTION: Verilator: Implementation of Christofides' algorithm to
// approximate the solution to the traveling salesman problem.
//
// ISSUES: This isn't exactly Christofides algorithm; see the TODO
// in perfectMatching(). True minimum-weight perfect matching
// would produce a better result. How much better is TBD.
//
// Code available from: https://verilator.org
//
//*************************************************************************
//
// Copyright 2003-2020 by Wilson Snyder. This program is free software; you
// can redistribute it and/or modify it under the terms of either the GNU
// Lesser General Public License Version 3 or the Perl Artistic License
// Version 2.0.
// SPDX-License-Identifier: LGPL-3.0-only OR Artistic-2.0
//
//*************************************************************************
#include "config_build.h"
#include "verilatedos.h"
#include "V3Error.h"
#include "V3Global.h"
#include "V3File.h"
#include "V3Graph.h"
#include "V3TSP.h"
#include <cmath>
#include <list>
#include <memory>
#include <set>
#include <sstream>
#include <string>
#include <vector>
#include <unordered_set>
#include <unordered_map>
//######################################################################
// Support classes
namespace V3TSP {
static unsigned edgeIdNext = 0;
static void selfTestStates();
static void selfTestString();
VL_DEBUG_FUNC; // Declare debug()
} // namespace V3TSP
// Vertex that tracks a per-vertex key
template <typename T_Key> class TspVertexTmpl : public V3GraphVertex {
private:
T_Key m_key;
public:
TspVertexTmpl(V3Graph* graphp, const T_Key& k)
: V3GraphVertex{graphp}
, m_key{k} {}
virtual ~TspVertexTmpl() override {}
const T_Key& key() const { return m_key; }
private:
VL_UNCOPYABLE(TspVertexTmpl);
};
// TspGraphTmpl represents a complete graph, templatized to work with
// different T_Key types.
template <typename T_Key> class TspGraphTmpl : public V3Graph {
public:
// TYPES
typedef TspVertexTmpl<T_Key> Vertex;
// MEMBERS
typedef std::unordered_map<T_Key, Vertex*> VMap;
VMap m_vertices; // T_Key to Vertex lookup map
// CONSTRUCTORS
TspGraphTmpl()
: V3Graph{} {}
virtual ~TspGraphTmpl() override {}
// METHODS
void addVertex(const T_Key& key) {
const auto itr = m_vertices.find(key);
UASSERT(itr == m_vertices.end(), "Vertex already exists with same key");
Vertex* v = new Vertex(this, key);
m_vertices[key] = v;
}
// For purposes of TSP, we are using non-directional graphs.
// Map that onto the normally-directional V3Graph by creating
// a matched pairs of opposite-directional edges to represent
// each non-directional edge:
void addEdge(const T_Key& from, const T_Key& to, int cost) {
UASSERT(from != to, "Adding edge would form a loop");
Vertex* fp = findVertex(from);
Vertex* tp = findVertex(to);
// No need to dedup edges.
// The only time we may create duplicate edges is when
// combining the MST with the perfect-matched pairs,
// and in that case, we want to permit duplicate edges.
unsigned edgeId = ++V3TSP::edgeIdNext;
// Record the 'id' which identifies a single bidir edge
// in the user field of each V3GraphEdge:
(new V3GraphEdge(this, fp, tp, cost))->user(edgeId);
(new V3GraphEdge(this, tp, fp, cost))->user(edgeId);
}
bool empty() const { return m_vertices.empty(); }
std::list<Vertex*> keysToVertexList(const std::vector<T_Key>& odds) {
std::list<Vertex*> vertices;
for (unsigned i = 0; i < odds.size(); ++i) { vertices.push_back(findVertex(odds.at(i))); }
return vertices;
}
class EdgeCmp {
// Provides a deterministic compare for outgoing V3GraphEdge's
// to be used in Prim's algorithm below. Also used in the
// perfectMatching() routine.
public:
// CONSTRUCTORS
EdgeCmp() {}
// METHODS
bool operator()(const V3GraphEdge* ap, const V3GraphEdge* bp) {
int aCost = ap->weight();
int bCost = bp->weight();
// Sort first on cost, lowest cost edges first:
if (aCost < bCost) return true;
if (bCost < aCost) return false;
// Costs are equal. Compare edgeId's which should be unique.
return ap->user() < bp->user();
}
private:
VL_UNCOPYABLE(EdgeCmp);
};
static Vertex* castVertexp(V3GraphVertex* vxp) { return dynamic_cast<Vertex*>(vxp); }
// From *this, populate *mstp with the minimum spanning tree.
// *mstp must be initially empty.
void makeMinSpanningTree(TspGraphTmpl* mstp) {
UASSERT(mstp->empty(), "Output graph must start empty");
// Use Prim's algorithm to efficiently construct the MST.
std::unordered_set<Vertex*> visited_set;
EdgeCmp cmp;
typedef std::set<V3GraphEdge*, EdgeCmp&> PendingEdgeSet;
// This is the set of pending edges from visited to unvisited
// nodes.
PendingEdgeSet pendingEdges(cmp);
vluint32_t vertCount = 0;
for (V3GraphVertex* vxp = verticesBeginp(); vxp; vxp = vxp->verticesNextp()) {
mstp->addVertex(castVertexp(vxp)->key());
vertCount++;
}
// Choose an arbitrary start vertex and visit it;
// all incident edges from this vertex go into a pending edge set.
Vertex* start_vertexp = castVertexp(verticesBeginp());
visited_set.insert(start_vertexp);
for (V3GraphEdge* edgep = start_vertexp->outBeginp(); edgep; edgep = edgep->outNextp()) {
pendingEdges.insert(edgep);
}
// Repeatedly find the least costly edge in the pending set.
// If it connects to an unvisited node, visit that node and update
// the pending edge set. If it connects to an already visited node,
// discard it and repeat again.
unsigned edges_made = 0;
while (!pendingEdges.empty()) {
const auto firstIt = pendingEdges.cbegin();
V3GraphEdge* bestEdgep = *firstIt;
pendingEdges.erase(firstIt);
// bestEdgep->fromp() should be already seen
Vertex* from_vertexp = castVertexp(bestEdgep->fromp());
UASSERT(visited_set.find(from_vertexp) != visited_set.end(), "Can't find vertex");
// If the neighbor is not yet visited, visit it and add its edges
// to the pending set.
Vertex* neighborp = castVertexp(bestEdgep->top());
if (visited_set.find(neighborp) == visited_set.end()) {
int bestCost = bestEdgep->weight();
UINFO(6, "bestCost = " << bestCost << " from " << from_vertexp->key() << " to "
<< neighborp->key() << endl);
// Create the edge in our output MST graph
mstp->addEdge(from_vertexp->key(), neighborp->key(), bestCost);
edges_made++;
// Mark this vertex as visited
visited_set.insert(neighborp);
// Update the pending edges with new edges
for (V3GraphEdge* edgep = neighborp->outBeginp(); edgep;
edgep = edgep->outNextp()) {
pendingEdges.insert(edgep);
}
} else {
UINFO(6,
"Discarding edge to already-visited neighbor " << neighborp->key() << endl);
}
}
UASSERT(edges_made + 1 == vertCount, "Algorithm failed");
UASSERT(visited_set.size() == vertCount, "Algorithm failed");
}
// Populate *outp with a minimal perfect matching of *this.
// *outp must be initially empty.
void perfectMatching(const std::vector<T_Key>& oddKeys, TspGraphTmpl* outp) {
UASSERT(outp->empty(), "Output graph must start empty");
std::list<Vertex*> odds = keysToVertexList(oddKeys);
std::unordered_set<Vertex*> unmatchedOdds;
typedef typename std::list<Vertex*>::iterator VertexListIt;
for (VertexListIt it = odds.begin(); it != odds.end(); ++it) {
outp->addVertex((*it)->key());
unmatchedOdds.insert(*it);
}
UASSERT(odds.size() % 2 == 0, "number of odd-order nodes should be even");
// TODO: The true Chrisofides algorithm calls for minimum-weight
// perfect matching. Instead, we have a simple greedy algorithm
// which might get close to the minimum, maybe, with luck?
//
// TODO: Revisit this. It's possible to compute the true minimum in
// N*N*log(N) time using variants of the Blossom algorithm.
// Implementing Blossom looks hard, maybe we can use an existing
// open source implementation -- for example the "LEMON" library
// which has a TSP solver.
// -----
// Reuse the comparator from Prim's routine. The logic is the same
// here. Note that the two V3GraphEdge's representing a single
// bidir edge will collide in the pendingEdges set here, but this
// is OK, we'll ignore the direction on the edge anyway.
EdgeCmp cmp;
typedef std::set<V3GraphEdge*, EdgeCmp&> PendingEdgeSet;
PendingEdgeSet pendingEdges(cmp);
for (VertexListIt it = odds.begin(); it != odds.end(); ++it) {
for (V3GraphEdge* edgep = (*it)->outBeginp(); edgep; edgep = edgep->outNextp()) {
pendingEdges.insert(edgep);
}
}
// Iterate over all edges, in order from low to high cost.
// For any edge whose ends are both odd-order vertices which
// haven't been matched yet, match them.
for (typename PendingEdgeSet::iterator it = pendingEdges.begin(); it != pendingEdges.end();
++it) {
Vertex* fromp = castVertexp((*it)->fromp());
Vertex* top = castVertexp((*it)->top());
if ((unmatchedOdds.find(fromp) != unmatchedOdds.end())
&& (unmatchedOdds.find(top) != unmatchedOdds.end())) {
outp->addEdge(fromp->key(), top->key(), (*it)->weight());
unmatchedOdds.erase(fromp);
unmatchedOdds.erase(top);
}
}
UASSERT(unmatchedOdds.empty(), "Algorithm should have processed all vertices");
}
void combineGraph(const TspGraphTmpl& g) {
std::unordered_set<vluint32_t> edges_done;
for (V3GraphVertex* vxp = g.verticesBeginp(); vxp; vxp = vxp->verticesNextp()) {
Vertex* fromp = castVertexp(vxp);
for (V3GraphEdge* edgep = fromp->outBeginp(); edgep; edgep = edgep->outNextp()) {
Vertex* top = castVertexp(edgep->top());
if (edges_done.find(edgep->user()) == edges_done.end()) {
addEdge(fromp->key(), top->key(), edgep->weight());
edges_done.insert(edgep->user());
}
}
}
}
void findEulerTourRecurse(std::unordered_set<unsigned>* markedEdgesp, Vertex* startp,
std::vector<T_Key>* sortedOutp) {
Vertex* cur_vertexp = startp;
// Go on a random tour. Fun!
std::vector<Vertex*> tour;
do {
UINFO(6, "Adding " << cur_vertexp->key() << " to tour.\n");
tour.push_back(cur_vertexp);
// Look for an arbitrary edge we've not yet marked
for (V3GraphEdge* edgep = cur_vertexp->outBeginp(); edgep; edgep = edgep->outNextp()) {
vluint32_t edgeId = edgep->user();
if (markedEdgesp->end() == markedEdgesp->find(edgeId)) {
// This edge is not yet marked, so follow it.
markedEdgesp->insert(edgeId);
Vertex* neighborp = castVertexp(edgep->top());
UINFO(6, "following edge " << edgeId << " from " << cur_vertexp->key()
<< " to " << neighborp->key() << endl);
cur_vertexp = neighborp;
goto found;
}
}
v3fatalSrc("No unmarked edges found in tour");
found:;
} while (cur_vertexp != startp);
UINFO(6, "stopped, got back to start of tour @ " << cur_vertexp->key() << endl);
// Look for nodes on the tour that still have
// un-marked edges. If we find one, recurse.
for (Vertex* vxp : tour) {
bool recursed;
do {
recursed = false;
// Look for an arbitrary edge at vxp we've not yet marked
for (V3GraphEdge* edgep = vxp->outBeginp(); edgep; edgep = edgep->outNextp()) {
vluint32_t edgeId = edgep->user();
if (markedEdgesp->end() == markedEdgesp->find(edgeId)) {
UINFO(6, "Recursing.\n");
findEulerTourRecurse(markedEdgesp, vxp, sortedOutp);
recursed = true;
goto recursed;
}
}
recursed:;
} while (recursed);
sortedOutp->push_back(vxp->key());
}
UINFO(6, "Tour was: ");
for (const Vertex* vxp : tour) UINFONL(6, " " << vxp->key());
UINFONL(6, "\n");
}
void dumpGraph(std::ostream& os, const string& nameComment) const {
// UINFO(0) as controlled by caller
os << "At " << nameComment << ", dumping graph. Keys:\n";
for (V3GraphVertex* vxp = verticesBeginp(); vxp; vxp = vxp->verticesNextp()) {
Vertex* tspvp = castVertexp(vxp);
os << " " << tspvp->key() << endl;
for (V3GraphEdge* edgep = tspvp->outBeginp(); edgep; edgep = edgep->outNextp()) {
Vertex* neighborp = castVertexp(edgep->top());
os << " has edge " << edgep->user() << " to " << neighborp->key() << endl;
}
}
}
void dumpGraphFilePrefixed(const string& nameComment) const {
if (v3Global.opt.dumpTree()) {
string filename = v3Global.debugFilename(nameComment) + ".txt";
const std::unique_ptr<std::ofstream> logp(V3File::new_ofstream(filename));
if (logp->fail()) v3fatal("Can't write " << filename);
dumpGraph(*logp, nameComment);
}
}
void findEulerTour(std::vector<T_Key>* sortedOutp) {
UASSERT(sortedOutp->empty(), "Output graph must start empty");
if (debug() >= 6) dumpDotFilePrefixed("findEulerTour");
std::unordered_set<unsigned /*edgeID*/> markedEdges;
// Pick a start node
Vertex* start_vertexp = castVertexp(verticesBeginp());
findEulerTourRecurse(&markedEdges, start_vertexp, sortedOutp);
}
std::vector<T_Key> getOddDegreeKeys() const {
std::vector<T_Key> result;
for (V3GraphVertex* vxp = verticesBeginp(); vxp; vxp = vxp->verticesNextp()) {
Vertex* tspvp = castVertexp(vxp);
vluint32_t degree = 0;
for (V3GraphEdge* edgep = vxp->outBeginp(); edgep; edgep = edgep->outNextp()) {
degree++;
}
if (degree & 1) { result.push_back(tspvp->key()); }
}
return result;
}
private:
Vertex* findVertex(const T_Key& key) const {
const auto it = m_vertices.find(key);
UASSERT(it != m_vertices.end(), "Vertex not found");
return it->second;
}
VL_UNCOPYABLE(TspGraphTmpl);
};
//######################################################################
// Main algorithm
void V3TSP::tspSort(const V3TSP::StateVec& states, V3TSP::StateVec* resultp) {
UASSERT(resultp->empty(), "Output graph must start empty");
// Make this TSP implementation work for graphs of size 0 or 1
// which, unfortunately, is a special case as the following
// code assumes >= 2 nodes.
if (states.empty()) { return; }
if (states.size() == 1) {
resultp->push_back(*(states.begin()));
return;
}
// Build the initial graph from the starting state set.
typedef TspGraphTmpl<const TspStateBase*> Graph;
Graph graph;
for (V3TSP::StateVec::const_iterator it = states.begin(); it != states.end(); ++it) {
graph.addVertex(*it);
}
for (V3TSP::StateVec::const_iterator it = states.begin(); it != states.end(); ++it) {
for (V3TSP::StateVec::const_iterator jt = it; jt != states.end(); ++jt) {
if (it == jt) continue;
graph.addEdge(*it, *jt, (*it)->cost(*jt));
}
}
// Create the minimum spanning tree
Graph minGraph;
graph.makeMinSpanningTree(&minGraph);
if (debug() >= 6) minGraph.dumpGraphFilePrefixed("minGraph");
std::vector<const TspStateBase*> oddDegree = minGraph.getOddDegreeKeys();
Graph matching;
graph.perfectMatching(oddDegree, &matching);
if (debug() >= 6) matching.dumpGraphFilePrefixed("matching");
// Adds edges to minGraph, the resulting graph will have even number of
// edge counts at every vertex:
minGraph.combineGraph(matching);
V3TSP::StateVec prelim_result;
minGraph.findEulerTour(&prelim_result);
UASSERT(prelim_result.size() >= states.size(), "Algorithm size error");
// Discard duplicate nodes that the Euler tour might contain.
{
std::unordered_set<const TspStateBase*> seen;
for (V3TSP::StateVec::iterator it = prelim_result.begin(); it != prelim_result.end();
++it) {
const TspStateBase* elemp = *it;
if (seen.find(elemp) == seen.end()) {
seen.insert(elemp);
resultp->push_back(elemp);
}
}
}
UASSERT(resultp->size() == states.size(), "Algorithm size error");
// Find the most expensive arc and rotate the list so that the most
// expensive arc connects the last and first elements. (Since we're not
// modeling something that actually cycles back, we don't need to pay
// that cost at all.)
{
unsigned max_cost = 0;
unsigned max_cost_idx = 0;
for (unsigned i = 0; i < resultp->size(); ++i) {
const TspStateBase* ap = (*resultp)[i];
const TspStateBase* bp
= (i + 1 == resultp->size()) ? (*resultp)[0] : (*resultp)[i + 1];
unsigned cost = ap->cost(bp);
if (cost > max_cost) {
max_cost = cost;
max_cost_idx = i;
}
}
if (max_cost_idx == resultp->size() - 1) {
// List is already rotated for minimum cost. stop.
return;
}
V3TSP::StateVec new_result;
unsigned i = max_cost_idx + 1;
UASSERT(i < resultp->size(), "Algorithm size error");
while (i != max_cost_idx) {
new_result.push_back((*resultp)[i]);
i++;
if (i >= resultp->size()) { i = 0; }
}
new_result.push_back((*resultp)[i]);
UASSERT(resultp->size() == new_result.size(), "Algorithm size error");
*resultp = new_result;
}
}
//######################################################################
// Self Tests
class TspTestState : public V3TSP::TspStateBase {
public:
TspTestState(unsigned xpos, unsigned ypos)
: m_xpos{xpos}
, m_ypos{ypos}
, m_serial{++m_serialNext} {}
~TspTestState() {}
virtual int cost(const TspStateBase* otherp) const override {
return cost(dynamic_cast<const TspTestState*>(otherp));
}
static unsigned diff(unsigned a, unsigned b) {
if (a > b) return a - b;
return b - a;
}
virtual int cost(const TspTestState* otherp) const {
// For test purposes, each TspTestState is merely a point
// on the Cartesian plane; cost is the linear distance
// between two points.
unsigned xabs;
unsigned yabs;
xabs = diff(otherp->m_xpos, m_xpos);
yabs = diff(otherp->m_ypos, m_ypos);
return lround(sqrt(xabs * xabs + yabs * yabs));
}
unsigned xpos() const { return m_xpos; }
unsigned ypos() const { return m_ypos; }
bool operator<(const TspStateBase& other) const override {
return operator<(dynamic_cast<const TspTestState&>(other));
}
bool operator<(const TspTestState& other) const { return m_serial < other.m_serial; }
private:
unsigned m_xpos;
unsigned m_ypos;
unsigned m_serial;
static unsigned m_serialNext;
};
unsigned TspTestState::m_serialNext = 0;
void V3TSP::selfTestStates() {
// Linear test -- coords all along the x-axis
{
V3TSP::StateVec states;
TspTestState s10(10, 0);
TspTestState s60(60, 0);
TspTestState s20(20, 0);
TspTestState s100(100, 0);
TspTestState s5(5, 0);
states.push_back(&s10);
states.push_back(&s60);
states.push_back(&s20);
states.push_back(&s100);
states.push_back(&s5);
V3TSP::StateVec result;
tspSort(states, &result);
V3TSP::StateVec expect;
expect.push_back(&s100);
expect.push_back(&s60);
expect.push_back(&s20);
expect.push_back(&s10);
expect.push_back(&s5);
if (VL_UNCOVERABLE(expect != result)) {
for (V3TSP::StateVec::iterator it = result.begin(); it != result.end(); ++it) {
const TspTestState* statep = dynamic_cast<const TspTestState*>(*it);
cout << statep->xpos() << " ";
}
cout << endl;
v3fatalSrc("TSP linear self-test fail. Result (above) did not match expectation.");
}
}
// Second test. Coords are distributed in 2D space.
// Test that tspSort() will rotate the list for minimum cost.
{
V3TSP::StateVec states;
TspTestState a(0, 0);
TspTestState b(100, 0);
TspTestState c(200, 0);
TspTestState d(200, 100);
TspTestState e(150, 150);
TspTestState f(0, 150);
TspTestState g(0, 100);
states.push_back(&a);
states.push_back(&b);
states.push_back(&c);
states.push_back(&d);
states.push_back(&e);
states.push_back(&f);
states.push_back(&g);
V3TSP::StateVec result;
tspSort(states, &result);
V3TSP::StateVec expect;
expect.push_back(&f);
expect.push_back(&g);
expect.push_back(&a);
expect.push_back(&b);
expect.push_back(&c);
expect.push_back(&d);
expect.push_back(&e);
if (VL_UNCOVERABLE(expect != result)) {
for (V3TSP::StateVec::iterator it = result.begin(); it != result.end(); ++it) {
const TspTestState* statep = dynamic_cast<const TspTestState*>(*it);
cout << statep->xpos() << "," << statep->ypos() << " ";
}
cout << endl;
v3fatalSrc(
"TSP 2d cycle=false self-test fail. Result (above) did not match expectation.");
}
}
}
void V3TSP::selfTestString() {
typedef TspGraphTmpl<string> Graph;
Graph graph;
graph.addVertex("0");
graph.addVertex("1");
graph.addVertex("2");
graph.addVertex("3");
graph.addEdge("0", "1", 3943);
graph.addEdge("0", "2", 3456);
graph.addEdge("0", "3", 4920);
graph.addEdge("1", "2", 2730);
graph.addEdge("1", "3", 8199);
graph.addEdge("2", "3", 4130);
Graph minGraph;
graph.makeMinSpanningTree(&minGraph);
if (debug() >= 6) minGraph.dumpGraphFilePrefixed("minGraph");
std::vector<string> oddDegree = minGraph.getOddDegreeKeys();
Graph matching;
graph.perfectMatching(oddDegree, &matching);
if (debug() >= 6) matching.dumpGraphFilePrefixed("matching");
minGraph.combineGraph(matching);
std::vector<string> result;
minGraph.findEulerTour(&result);
std::vector<string> expect;
expect.push_back("0");
expect.push_back("2");
expect.push_back("1");
expect.push_back("2");
expect.push_back("3");
if (VL_UNCOVERABLE(expect != result)) {
for (const string& i : result) cout << i << " ";
cout << endl;
v3fatalSrc("TSP string self-test fail. Result (above) did not match expectation.");
}
}
void V3TSP::selfTest() {
selfTestString();
selfTestStates();
}
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