files for PSA01

PSA01/cities128.dat

+4.470802 -1.871527
+-3.031774 1.549377
+7.894372 2.928784
+10.321351 -3.490053
+0.534141 -1.425673
+5.245451 2.888229
+0.027076 4.315900
+10.085365 -2.872810
+-9.584009 4.365102
+-10.437469 -5.304982
+-10.459263 4.861448
+7.939559 -2.733902
+8.744194 1.447623
+1.480710 -1.101613
+-2.749660 2.498327
+7.262462 3.714656
+-8.293333 1.769513
+7.320706 2.824994
+-5.063172 4.331169
+-2.904489 0.980203
+-10.571174 -0.320163
+0.294089 -0.043147
+-5.212059 4.574710
+-8.738593 -0.670101
+9.374125 1.672909
+-4.407383 -0.483221
+9.705810 -4.398309
+-1.623478 -0.740097
+-8.052749 0.157121
+-4.516453 -3.180130
+-3.194269 0.916789
+-9.707856 5.021509
+5.249016 -1.522861
+8.035496 1.810677
+-7.345268 1.834054
+-7.949954 -4.082847
+-10.124908 -3.121888
+-11.080439 0.154886
+6.951096 -2.473320
+-4.811675 -3.625790
+0.070514 -5.575789
+-6.066796 0.698825
+-10.061157 -1.079548
+10.407074 2.759780
+4.698264 -4.522170
+0.608994 2.590193
+7.941049 -4.122449
+8.184578 1.571563
+-0.198618 0.247553
+-8.588731 -1.558276
+11.173092 3.597192
+2.902615 1.271134
+-10.926899 -3.346488
+9.853496 2.998616
+-0.646473 1.521443
+-11.194432 0.452273
+5.011800 -2.625334
+0.250094 0.460775
+10.927726 0.394153
+3.098638 -0.937429
+6.537779 -3.624053
+9.158989 5.387815
+4.741745 -2.591301
+7.699449 -1.629041
+9.445726 6.029175
+-7.391364 4.214542
+2.429028 1.782166
+-4.582008 3.043505
+0.234214 4.717863
+-0.439387 -3.906525
+-8.674616 2.373730
+-1.418618 1.220522
+0.851148 3.367162
+-8.267115 2.672558
+6.798563 1.136338
+2.867453 0.118816
+5.990139 -3.459365
+0.242416 -3.584069
+3.353172 0.564160
+8.369109 4.087135
+-7.979719 2.604741
+8.663288 2.113997
+-0.376275 0.647530
+9.449945 -3.536561
+-7.688408 0.326020
+10.912657 -4.324923
+-1.008561 2.133955
+-7.461632 -3.296200
+3.706442 0.974182
+10.008075 4.060943
+6.769445 3.636326
+-3.984799 1.411626
+-5.074461 2.961612
+3.335316 1.043352
+2.451567 -1.854812
+-9.268376 1.689952
+-9.534869 -0.363558
+-10.400661 -3.115979
+-5.686984 -3.448522
+11.328903 0.718192
+-7.102361 -4.577878
+1.576087 -0.268046
+10.341826 -3.156231
+10.168671 -6.883715
+9.987043 -6.092928
+-7.378438 2.143717
+4.886129 4.239258
+7.431826 2.188098
+-4.919944 6.105738
+0.401401 0.886585
+-7.900566 0.347154
+2.820183 -0.558944
+4.355351 4.419650
+8.098856 3.225768
+-2.937645 0.460572
+-2.624444 2.006121
+5.232943 -3.947831
+-1.738663 -0.144068
+-9.058603 -0.079247
+-0.145825 -5.568225
+11.116066 -3.126504
+-9.932385 5.977374
+10.650692 -3.538089
+-8.191760 2.247480
+3.919696 2.594774
+2.215149 3.349125
+-10.453925 -5.780264
+-9.333344 4.971423

PSA01/omp_5center.c

+#include <stdio.h>
+#include <stdlib.h>
+#include <float.h>
+#include <math.h>
+#include <omp.h>
+
+#define MAX_POINTS 2000
+
+// read the file of points
+int read_file (float points[], char* filename) {
+
+    int n = 0;
+    float next[2];
+    FILE* file_ptr;
+    file_ptr = fopen(filename,"r");
+    if (file_ptr == NULL) {
+        printf ("error : could not open file %s for reading\n",filename);
+        exit(1);
+    }
+    while (fscanf (file_ptr,"%f %f",next,next+1) == 2) {
+        if (n < MAX_POINTS) {
+            points[2*n] = next[0];
+            points[2*n+1] = next[1];
+            n += 1;
+        } else {
+            printf ("Too many points in file %s\n",filename);
+            fclose (file_ptr);
+            exit(1);
+        }
+    }
+    fclose (file_ptr);
+    return n;
+}
+
+// calculate the distance squared between two points
+float calc_dist_sq (float u[], float v[]) {
+    float diff_x = u[0] - v[0];
+    float diff_y = u[1] - v[1];
+    return (diff_x*diff_x + diff_y*diff_y);
+}
+
+typedef struct centers_s {
+    int c[5];
+} centers_type;
+
+// compute the cost squared for centers in the centers array
+float center_cost_sq (float dist_sqs[], int n, centers_type check, float min_cost_sq) {
+    float cost_sq = 0;
+    for (int i=0;i<n;i++) {
+        float dist_sq_1 = dist_sqs[i*n+check.c[0]];
+        float dist_sq_2 = dist_sqs[i*n+check.c[1]];
+        float dist_sq_3 = dist_sqs[i*n+check.c[2]];
+        float dist_sq_4 = dist_sqs[i*n+check.c[3]];
+        float dist_sq_5 = dist_sqs[i*n+check.c[4]];
+        float min_dist_sq = dist_sq_1;
+        if (dist_sq_2 < min_dist_sq) {
+            min_dist_sq = dist_sq_2;
+        }
+        if (dist_sq_3 < min_dist_sq) {
+            min_dist_sq = dist_sq_3;
+        }
+        if (dist_sq_4 < min_dist_sq) {
+            min_dist_sq = dist_sq_4;
+        }
+        if (dist_sq_5 < min_dist_sq) {
+            min_dist_sq = dist_sq_5;
+        }
+        // check to see if we can abort early
+        if (min_dist_sq > min_cost_sq) {
+            return min_dist_sq;
+        }
+        if (min_dist_sq > cost_sq) {
+            cost_sq = min_dist_sq;
+        }
+    }
+    return cost_sq;
+}
+
+// solve the 5-center problem exactly
+// returns the minimal cost and an optimal set of 5 centers
+double solve_5center (float dist_sqs[], int n, centers_type* optimal, long int* num_checked) {
+
+    double min_cost_sq = DBL_MAX;
+    *num_checked = 0;
+    for (int i=0;i<n-4;i++) {
+        for (int j=i+1;j<n-3;j++) {
+            for (int k=j+1;k<n-2;k++) {
+                for (int l=k+1;l<n-1;l++) {
+                    for (int m=l+1;m<n;m++) {
+                        *num_checked += 1;
+                        centers_type check = { i, j, k, l, m };
+                        double cost_sq = center_cost_sq (dist_sqs,n,check,min_cost_sq);
+                        if (cost_sq < min_cost_sq) {
+                            min_cost_sq = cost_sq;
+                            *optimal = check;
+                        }
+                    }
+                }
+            }
+        }
+    }
+    // return the minimal cost
+    return sqrt(min_cost_sq);
+}
+
+int main (int argc, char** argv) {
+
+    // the points array
+    float points[2*MAX_POINTS];
+
+    // read filename and thread count from command line
+    if (argc < 3) {
+        printf ("Command usage : %s %s %s\n",argv[0],"filename","thread_count");
+        return 1;
+    }
+    int thread_count = atoi(argv[2]);
+    omp_set_num_threads(thread_count);
+
+    // read dataset
+    int n = read_file (points,argv[1]);
+
+    // calculate the distances squared table
+    float dist_sqs[n*n];
+    for (int i=0;i<n;i++) {
+        for (int j=0;j<n;j++) {
+            dist_sqs[i*n+j] = calc_dist_sq (points+2*i,points+2*j);
+        }
+    }
+
+    // print the number of points and number of threads
+    printf ("number of points = %d, number of threads = %d\n",n,thread_count);
+
+    // start the timer
+    double start_time, end_time;
+    start_time = omp_get_wtime();
+
+    // solve the 5-center problem exactly
+    centers_type optimal;
+    long int num_checked;
+    double min_cost = solve_5center (dist_sqs,n,&optimal,&num_checked);
+
+    // stop the timer
+    end_time = omp_get_wtime();
+    double elapsed = end_time-start_time;
+
+    // print out the number of 5-tuples checked
+    printf ("Total 5-tuples checked = %ld\n",num_checked);
+
+    // print the minimal cost for the 5-center problem
+    printf ("minimal cost = %g\n",min_cost);
+
+    // print an optimal solution to the 5-center problem
+    printf ("optimal centers : %d %d %d %d %d\n",optimal.c[0],optimal.c[1],
+            optimal.c[2],optimal.c[3],optimal.c[4]);
+
+    // print the elapsed time
+    printf ("elapsed time = %g seconds\n",elapsed);
+
+    // print the tuples checked per second
+    printf ("5-tuples checked per second = %.0lf\n",num_checked/elapsed);
+
+}