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fastwvc.cpp
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fastwvc.cpp
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#include <algorithm>
#include <chrono>
#include <iostream>
#include <random>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using namespace chrono;
typedef pair<int, int> pii;
typedef vector<bool> vb;
typedef vector<int> vi;
struct edge {
int u;
int v;
};
bool debug = false;
int INF = 1e9;
int n, e;
vi node_weights;
vi node_degrees;
vector<edge> edge_list;
vector<vector<pii>> AL; // pair is (neighbour, edge_index)
int best_weight = INF;
vb best_cover;
int step_cover_weight;
vb step_cover;
int step = 0;
vb node_conf_change;
vi node_dscores;
vi edge_weights;
vb tabu_list;
vi remove_candidates;
vi timestamp;
unordered_set<int> uncovered_edges;
// these variables are used for an extension which is not implemented for now
int avg_weight = 1;
int delta_total_weight = 0;
double p_scale = 0.3;
int threshold;
/* DEBUGGING METHODS */
void print_vi(vi &v, string name) {
cout << name << ": ";
for (auto &i : v) {
cout << i << " ";
}
cout << endl;
}
void print_vb(vb &v, string name) {
cout << name << ": ";
for (const auto &b : v) {
cout << b; // Automatically converts to 1 or 0
}
cout << endl;
}
void print_set(unordered_set<int> &s, string name) {
cout << name << ": ";
for (const auto &i : s) {
cout << i << ' ';
}
cout << endl;
}
// generates a good initial candidate using ConstructMWVC
void init_mwvc() {
int best_weight_init = INF;
vb best_cover_init(n, false);
// 1. generate a first "draft" greedily by iterating through edges and
// picking the node with better weight to degree ratio
int curr_weight = 0;
vb curr_cover(n, false);
for (edge e : edge_list) {
if (!curr_cover[e.u] && !curr_cover[e.v]) {
double degreeU = (double)node_degrees[e.u] / (double)node_weights[e.u];
double degreeV = (double)node_degrees[e.v] / (double)node_weights[e.v];
// choose the endpoint with larger degree/weight to be added
int better_node = degreeU > degreeV ? e.u : e.v;
curr_weight += node_weights[better_node];
curr_cover[better_node] = true;
}
}
best_weight_init = curr_weight;
best_cover_init = curr_cover;
// 2. repeated extending phase. first split the edges into blocks
vi blocks(e / 1024 + 1);
for (int i = 0; i < e / 1024 + 1; i++) {
blocks[i] = i;
}
int tries = 50;
while (--tries >= 0) {
curr_weight = 0;
curr_cover = vb(n, false);
// shuffle order of blocks
shuffle(blocks.begin(), blocks.end(), default_random_engine(0));
for (int block_id : blocks) {
int begin = block_id * 1024;
int end = block_id == e / 1024 ? e - 1 : begin + 1024;
int block_size = end - begin + 1;
vi idx(block_size); // holds edge indices within the current block
for (int i = 0; i < block_size; i++) {
idx[i] = begin + i;
}
while (block_size > 0) {
int i = rand() % block_size;
edge edge = edge_list[idx[i]];
int u = edge.u, v = edge.v;
block_size--;
swap(idx[i], idx[block_size]);
// if both endpoints are not in cover, add the better one
if (!curr_cover[u] && !curr_cover[v]) {
double degreeU = (double)node_degrees[u] / (double)node_weights[u];
double degreeV = (double)node_degrees[v] / (double)node_weights[v];
int better_node = degreeU > degreeV ? u : v;
curr_weight += node_weights[better_node];
curr_cover[better_node] = true;
}
}
}
if (curr_weight < best_weight_init) {
best_weight_init = curr_weight;
best_cover_init = curr_cover;
}
}
// 3. shrinking phase
// harm_values[i] = if node i is removed from the cover, how many edges
// would become uncovered aka number of edges that are solely covered by it
vi harm_values(n, 0);
for (int i = 0; i < e; i++) {
edge edge = edge_list[i];
if (best_cover_init[edge.u] && !best_cover_init[edge.v]) {
harm_values[edge.u]++;
}
if (best_cover_init[edge.v] && !best_cover_init[edge.u]) {
harm_values[edge.v]++;
}
}
// remove nodes from cover if harm value is 0
for (int i = 0; i < n; i++) {
if (best_cover_init[i] && harm_values[i] == 0) {
best_cover_init[i] = false;
best_weight_init -= node_weights[i];
for (pii p : AL[i]) {
int neighbour = p.first;
harm_values[neighbour]++; // neighbour is now responsible for
// covering one more edge
}
}
}
// set this result as global optimal (for now)
best_weight = best_weight_init;
best_cover = best_cover_init;
}
// calculate the initial dscore values based on init candidate, for calculating
// gain / loss initially, all are loss values since all edges are initially
// covered, hence dscores are neg
void generate_dscores_init() {
for (int i = 0; i < e; i++) {
edge edge = edge_list[i];
// edges that are covered by only one node constribute to the node's
// dscore if the edge becomes uncovered, cost will increase by the edge
// weight
if (best_cover[edge.u] && !best_cover[edge.v]) {
node_dscores[edge.u] -= edge_weights[i];
} else if (!best_cover[edge.u] && best_cover[edge.v]) {
node_dscores[edge.v] -= edge_weights[i];
}
}
}
// generate an initial list of nodes that are part of the cover, to be
// maintained throughout the algorithm for ease of iterating through nodes that
// are part of the cover
void generate_remove_candidates() {
for (int i = 0; i < n; i++) {
if (best_cover[i]) {
remove_candidates.push_back(i);
}
}
}
// in reference implementation, removal is O(1) by tracking indices, but O(n) is chosen for
// simplicity and because it is theoretically not crucial, as complexity of other steps outweighs
// this
void remove_node(int node, int &step_cover_weight, vb &step_cover) {
if (debug) cout << "remove node " << node << endl;
// remove from the current step cover
step_cover_weight -= node_weights[node];
step_cover[node] = false;
remove_candidates.erase(remove(remove_candidates.begin(), remove_candidates.end(), node),
remove_candidates.end());
node_dscores[node] = -node_dscores[node]; // now adding it will cover X amount of edges
node_conf_change[node] = false;
// update node_dscores and node_conf_change of neighbours
for (pii p : AL[node]) {
int neighbour = p.first, edge_idx = p.second;
if (debug)
cout << "initial dscore of " << neighbour << " = " << node_dscores[neighbour] << endl;
node_conf_change[neighbour] = true;
if (step_cover[neighbour]) {
node_dscores[neighbour] -= edge_weights[edge_idx]; // neighbour has more responsibility
} else {
node_dscores[neighbour] += edge_weights[edge_idx];
node_conf_change[neighbour] = true; // neighbour eligible to be added into cover
uncovered_edges.insert(edge_idx);
}
if (debug)
cout << "new dscore of " << neighbour << " = " << node_dscores[neighbour] << endl;
}
}
// basically the opposite of remove_node
void add_node(int node, int &step_cover_weight, vb &step_cover) {
step_cover_weight += node_weights[node];
step_cover[node] = true;
remove_candidates.push_back(node);
node_dscores[node] = -node_dscores[node];
// don't need to set it's own conf_change, only need to set when removing
for (pii p : AL[node]) {
int neighbour = p.first, edge_idx = p.second;
if (step_cover[neighbour]) {
node_dscores[neighbour] += edge_weights[edge_idx];
} else {
node_dscores[neighbour] -= edge_weights[edge_idx];
node_conf_change[neighbour] = true;
uncovered_edges.erase(edge_idx);
}
}
}
// main step funciton for local search. at every step, remove 2 nodes and try to reconstruct
void step_function() {
// remove the first node by greedily choosing the one with smallest loss
if (debug) print_vi(remove_candidates, "remove_candidates");
double smallest_loss = INF;
int node_to_remove_1 = remove_candidates[0];
for (int i = 0; i < remove_candidates.size(); i++) {
int node = remove_candidates[i];
double loss = (double)abs(node_dscores[node]) / (double)node_weights[node];
if (loss < smallest_loss) {
smallest_loss = loss;
node_to_remove_1 = node;
}
}
remove_node(node_to_remove_1, step_cover_weight, step_cover);
// choose second node to remove using BMS strategy (biased memory saving)
int tries = 100;
// use same variable node_to_remove from before
int idx = rand() % remove_candidates.size();
int node_to_remove_2 = remove_candidates[idx];
double current_loss =
(double)abs(node_dscores[node_to_remove_2]) / (double)node_weights[node_to_remove_2];
while (--tries >= 0) {
int node = remove_candidates[rand() % remove_candidates.size()];
double loss = (double)abs(node_dscores[node]) / (double)node_weights[node];
if (tabu_list[node]) continue;
if (loss > current_loss) continue;
if (loss < current_loss) {
node_to_remove_2 = node;
current_loss = loss;
} else if (timestamp[node] < timestamp[node_to_remove_2]) { // tiebreak by timestamp
node_to_remove_2 = node;
current_loss = loss;
}
}
remove_node(node_to_remove_2, step_cover_weight, step_cover);
if (debug) print_set(uncovered_edges, "uncovered_edges");
tabu_list = vb(n, false);
while (!uncovered_edges.empty()) {
int node_to_add = 0;
double best_gain = 0;
// choose a vertex to add, considering both recently removed nodes
for (int consider : {node_to_remove_1, node_to_remove_2}) {
// consider its neighbours
for (pii p : AL[consider]) {
int neighbour = p.first;
if (step_cover[neighbour] || node_conf_change[neighbour] == false) continue;
double gain = (double)node_dscores[neighbour] / (double)node_weights[neighbour];
if (gain > best_gain) {
best_gain = gain;
node_to_add = neighbour;
} else if (gain == best_gain && timestamp[neighbour] < timestamp[node_to_add]) {
node_to_add = neighbour;
}
}
// consider the node itself
if (node_conf_change[consider] && !step_cover[consider]) {
int gain = (double)node_dscores[consider] / (double)node_weights[consider];
if (gain > best_gain) {
best_gain = gain;
node_to_add = consider;
} else if (gain == best_gain && timestamp[consider] < timestamp[node_to_add]) {
node_to_add = consider;
}
}
}
add_node(node_to_add, step_cover_weight, step_cover);
if (debug) cout << "added node " << node_to_add << endl;
if (debug) print_set(uncovered_edges, "uncovered_edges");
tabu_list[node_to_add] = true;
timestamp[node_to_add] = step;
// update edge weights of uncovered edges
for (auto &edge_idx : uncovered_edges) {
edge edge = edge_list[edge_idx];
edge_weights[edge_idx]++;
node_dscores[edge.u]++;
node_dscores[edge.v]++;
}
}
// remove redundant nodes
for (int node : remove_candidates) {
if (step_cover[node] && node_dscores[node] == 0) {
remove_node(node, step_cover_weight, step_cover);
}
}
// update cover if improves
if (step_cover_weight < best_weight) {
best_weight = step_cover_weight;
best_cover = step_cover;
}
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
auto end_time = high_resolution_clock::now() + milliseconds(1995);
// read input and initialise structures
cin >> n >> e;
AL = vector<vector<pii>>(n, vector<pii>());
best_cover = vb(n, false);
node_weights = vi(n, 0);
node_dscores = vi(n, 0);
node_conf_change = vb(n, false);
edge_list = vector<edge>(e);
node_degrees = vi(n, 0);
edge_weights = vi(e, 1);
tabu_list = vb(n, false);
timestamp = vi(n, 0);
threshold = (int)(0.5 * n);
for (int i = 0; i < n; i++) {
cin >> node_weights[i];
node_conf_change[i] = true;
}
for (int i = 0; i < e; i++) {
int u, v;
cin >> u >> v;
AL[u].push_back(make_pair(v, i));
AL[v].push_back(make_pair(u, i));
edge_list[i].u = u;
edge_list[i].v = v;
node_degrees[u]++;
node_degrees[v]++;
}
init_mwvc();
generate_dscores_init();
generate_remove_candidates();
step_cover_weight = best_weight;
step_cover = best_cover;
while (high_resolution_clock::now() < end_time) {
step_function();
step++;
}
cout << best_weight << endl;
for (int i = 0; i < n; i++) {
if (best_cover[i]) cout << i << " ";
}
cout << endl;
return 0;
}