IMPORTANT REMINDERS. Code-packaging info for your tar file. Other reminders, FYI

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1 Carnegie Mellon University Multimedia Databases and Data Mining Spring 2016, C. Faloutsos Homework 2 Due Date: Feb. 3, 3:00pm, in class Designed by: Di Jin. IMPORTANT REMINDERS All homeworks are to be done INDIVIDUALLY. All written answers should be TYPED. For each question, we expect both a hard copy, as specified per question, as well as a tar file with your code - see details next, on how to package your code. Code-packaging info for your tar file Submit your code to blackboard, in a single tar file, called andrewid-hw2.tar.gz. For your convenience, we provide a tar-file package, at courses/826.s16/homeworks/hw2/christos-hw2.tar.gz. It has 4 directories /Q1, /Q2, /Q3, /Q4, the k-d-tree and R-tree source code, and place-holder code. TO DO: tar xvfz christos-hw2.tar.gz; cd Q1; make # to work on kdtrees Replace the place-holder code with your solutions, tar everything into andrewid-hw2.tar.gz and submit to blackboard. Hints: Please explore the makefiles we have created, for your convenience. For example, from the top directory: make hw2 will run the code for all 4 questions make package will try create the tar-file, for submission make spotless will clean up all the derived files (*.o, etc) Reminders: Make sure that you 1. exclude redundant/derived files, in your tar-file 2. test your tar file (tar xvf; make hw2), to check for omitted files. Other reminders, FYI Expected effort for this homework: total of hours ( 4-8 hours per question). Weight: 30% of total homeworks weight = 3% of course weight. 1

2 Q1 KD-Trees [40pts] Print answers on separate page, with [course-id] [hw#] [question#] [andrew-id] [your name] Grading info: graded by Varshaa Naganathan Problem Description: Consider the k-d-tree package, in C, in the directory./q1 of the provided tar-file package. We want to add the range-knn query, with parameters k and r, which is an extension of the nearest-neighbor query: it should return the k nearest neighbors, as long as they are within radius r. If the tree has fewer than k qualifying nodes then we should return all the nodes, with a warning: only <number> nodes found. Input Format: We will use m as the code for the new query (since n is taken, for the nearest-neighbor query). For your coding convenience, we will fix k=5, and r= Thus, the query need only specify the d coordinates of the query point, for example, for a d=3 (ie., 3-dimensional setting), the lines m should return (at most) k=5 neighbors, as long as they are within r=0.002 from the query point (0.8, 0.8, 0.8). In fact, this is one of the queries in the included file 3d-input.txt. 1. [10 pt] Augment the provided kdtree code, to handle such range-knn queries, with k = 5 nearest neighbors within the range of r = [10 pt] Testing: We plan to test your code ourselves, on several secret settings (which, of course, we ll publish after the due date). Thus, test your code, for several other settings, of your design, to cover corner cases. Grading info: -2 for every wrong output 3. [20 pt] a hard copy of the output of your code, on the two included input scripts (2d-input.txt, 3d-input.txt; they are in the./q1 directory). In your output, keep only the lines that are the result of the range-knn queries, to save paper. (Hint: try grep -v ). For your convenience, try our makefile: make hw2 currently prints implement me, instead of the actual answer. Grading info: -2 for every wrong output What to turn in: Code: Submit your code to blackboard, in the./q1 directory of your tar.gz file. (Typing make hw2 should print your responses to the two input files, i.e., 2d-input.txt and 3d-input.txt.). Answers: Submit hard copy for 1. your code for Q the output of your code on the two input files 2

3 Solution: kdtree.c void mnnsearch (TREENODE subroot, VECTOR vp, int count ){ VECTOR best ; VECTOR bestarr [ count ] ; //#i f d e f DEBUG p r i n t f ( mnn t r e e search was c a l l e d with \n ) ; v e c p r i n t ( vp ) ; //#e n d i f int k ; int nodecounter = 0 ; int emptynodeflag = 0 ; for ( k=0;k<count ; k++) { best = rnnsearch ( subroot, vp, (VECTOR )NULL, 0 ) ; i f ( best!= NULL){ best >f l a g = TRUE; nodecounter += 1 ; else { emptynodeflag = 1 ; bestarr [ k ] = best ; for ( k=0;k<count ; k++) { best = bestarr [ k ] ; i f ( best!= NULL){ i f ( myvecdist2 ( best, vp ) < 0.002){ p r i n t f ( n e a r e s t neighbor %d :, k+1); v e c p r i n t ( best ) ; i f ( emptynodeflag==1){ p r i n t f ( Warning : only %d nodes found. \ n, nodecounter ) ; for ( k=0;k<count ; k++) { i f ( bestarr [ k ]!= NULL){ bestarr [ k] > f l a g = FALSE; 3

4 Solution: main.c case m : p r i n t f ( 5 nn with i n f i n i t y norm s e a r c h i n g... \ n ) ; count = 5 ; for ( i =0; i<numdims ; i ++){ p r i n t f ( %d th a t t r. value=, i ) ; s c a n f ( %l f, &val ) ; #i f d e f DEBUG p r i n t f ( %f \n, val ) ; #e n d i f vecput ( inputvectorptr, i, val ) ; #i f d e f DEBUG p r i n t f ( \ t \ t f o r %d nn\n, count ) ; #e n d i f p r i n t f ( nn s e a r c h i n g query point : ) ; v e c p r i n t ( inputvectorptr ) ; mnnsearch ( root, inputvectorptr, count ) ; break ; Solution: vector.c VECTOR v e c a l l o c ( VECTOR pvec ; int i ; int n){ a s s e r t ( n > 0 ) ; pvec = (VECTOR ) malloc ( sizeof (VECTOR) ) ; a s s e r t ( pvec!= NULL ) ; pvec > vec = (NUMBER ) malloc ( sizeof (NUMBER) n ) ; a s s e r t ( ( pvec >vec )!= NULL ) ; pvec >l e n = n ; / i n i t i a l i z e v e c t o r to z e r o s 2/7/97 / for ( i =0; i<n ; i ++){ ( pvec >vec ) [ i ] = (NUMBER) 0. 0 ; / i n i t i a l i z e f l a g to FALSE / pvec >f l a g = FALSE; return ( pvec ) ; 4

5 Q2 Z-order in mirrors [20pts] Print answers on separate page, with [course-id] [hw#] [question#] [andrew-id] [your name] Grading info: graded by Varshaa Naganathan Problem Description: A complete 2-dimension z order curve is centrosymmetric, where the center is the center of the whole plot (illustrated in Fig. 4). That is, if we rotate the curve by 180 degrees around its center, it will retain its shape. The mirror of point p is the point q, that p ends up landing, after such a rotation. In this problem, you will write the code to compute the (x,y) coordinates of the mirror point q, given the z-value of the point p. The command-line syntax should be: zmirror2 -n <order-of-curve> -i <integer> Thus: zmirror2 -n 2 -i 0 # should return 3 3 zmirror2 -n 3 -i 0 # should return see two blue squares in Figure 4 zmirror2 -n 3 -i 63 # should return 0 0 zmirror2 -n 3 -i 1 # should return 7 6 Figure 1: Examples of mirror pairs. The two blue squares are mirrors; and so are the two green crosses. The * marks the center of rotation. The weights are as follows: 1. [10 pt] Code: your zmirror2 should match the specifications. 2. [5 pt] Output: Give the results of your program on the input files./q2/q2.input.txt. Make sure you echo the input, so that it is clear which answer refers to which input. Grading info: -1 for x and y interchanged 5

6 3. [5 pt] Plot: Using your programs, write code to plot a z-curve of order 6 (64 * 64 grid) and dimension 2. For plotting, try gnuplot, as in the provided tar-file package. Hint: Make your code robust and guard against all the corner cases. E.g. negative coordinates, non-integer input, coordinates out of range, etc. For Q2.3, you could loop over the appropriate integers 0, 1,... and invoke your zmirror2 functionality. What to turn in: Code: Check the provided tar-file package, under directory./q2; replace the placeholder zmirror2.c, modify the makefile if necessary; and deliver 1. your code for Q2.1, 2. and Q2.3 Typing make hw2 should print your responses to the input files, and generate the plots for the z-curve. Answers: Hard copy of 1. your code for Q your code for Q2.2, 3. your output for Q2.2, 4. and your plot for Q2.3. 6

7 Solution: zmirror2.c #include zorder. h #include u t i l. h int main ( int argc, char argv ){ unsigned int x, y ; i f ( validargs ( argc, argv )!= 1){ p r i n t f ( Arguments e r r o r \n ) ; return 0 ; int input, order, max, mirror ; order = a t o i ( argv [ 2 ] ) ; input = a t o i ( argv [ 4 ] ) ; max = ( int )pow (2, order 2 ) ; mirror = (max 1) input ; i z o r d e r ( mirror, &x, &y ) ; p r i n t f ( %d %d\n, x, y ) ; return 0 ; 7

8 Solution: zorder.h #include <s t d i o. h> #include <math. h> #include <s t d l i b. h> #include <s t r i n g. h> int validargs ( int argc, char argv ) ; int unpart1by1 ( unsigned int n ) ; void i z o r d e r ( unsigned int z, unsigned int x, unsigned int y ) ; int checkcoor ( int input, int order ) ; int validargs ( int argc, char argv ){ i f ( argc!= 5){ return 1; int input = a t o i ( argv [ 4 ] ) ; int order = a t o i ( argv [ 2 ] ) ; i f ( checkcoor ( input, order ) < 0){ return 1; return 1 ; int unpart1by1 ( unsigned int n){ n&= 0 x ; n = (n ˆ ( n >> 1 ) ) & 0 x ; n = (n ˆ ( n >> 2 ) ) & 0 x 0 f 0 f 0 f 0 f ; n = (n ˆ ( n >> 4 ) ) & 0 x 0 0 f f 0 0 f f ; n = (n ˆ ( n >> 8 ) ) & 0 x f f f f ; return n ; void i z o r d e r ( unsigned int z, unsigned int x, unsigned int y ){ x = unpart1by1 ( z >> 1 ) ; y = unpart1by1 ( z ) ; 8

9 Solution: output for the input.txt./zmirror2 -n 3 -i 2 gives 6 7./zmirror2 -n 4 -i 6 gives /zmirror2 -n 5 -i 28 gives /zmirror2 -n 6 -i 4 gives /zmirror2 -n 6 -i 25 gives /zmirror2 -n 6 -i 40 gives Figure 2: Solution to the z-curve of order 6 (64 * 64 grid) and dimension 2 9

10 Q3 Hilbert Curve Plotting [10pts] Print answers on separate page, with [course-id] [hw#] [question#] [andrew-id] [your name] Grading info: graded by Zhoucheng Li Problem Description: The goal is to become familiar with Hilbert curves. We want code, to plot the Hilbert curve of order n. That is, hcurve -n 3 should plot Fig. 3(b), the Hilbert curve for the 8x8 grid. The output should be a.png file, like the one included in the tar-file package, under./q3 (a) Hilbert curve with order 2 (b) Hilbert curve with order 3 Figure 3: Hilbert curve examples Write programs to achieve the requirements; hand in your source code on hard copy; and submit your source code to blackboard. Weight distribution: 1. [5 pt] For your code, in C/C++. Grading info: -1 if order argument is hard coded -1 if there is tiny bug or logic error in code -5 if code is not attached -5 if code couldn t run 2. [5 pt] For the plot of a Hilbert curve of order 6 (64 * 64 grid) in 2-d. Again, we recommend gnuplot, but anything else that runs on the linux/andrew machines, is fine. Grading info: -1 if the graph has tiny error (e.g. part of the graph is out of box, is missing etc) -5 if the graph is not Hilber Curving plot to- 4 depends on the how the graph is close to answer Hint: For Hilbert curve, we recommend the code/algorithm from the following papers ( either one is fine - click on the citations, to get their pdf). Jagadish [SIGMOD 90] Roseman+ [PODS 89] 10

11 What to turn in: Code: Put your code for Q3.1 and Q3.2, under the directory./q3, replacing the placeholders we provide. Typing make hw2 should print the Hilbert curve of the specified order. Answers: Hard copy of 1. your code for Q your code Q and your plot for Q

12 Solution: horder.h #include <s t d i o. h> #include <math. h> #include <s t d l i b. h> #include <s t r i n g. h> int hcurve ; void r o t a t e ( int n, int x, int y, int rx, int ry ) ; int validargs ( int argc, char argv ) ; int checkcoor ( int coor, int order ) ; int validargs ( int argc, char argv ){ i f ( argc!= 5){ return 1; int input = a t o i ( argv [ 4 ] ) ; int order = a t o i ( argv [ 2 ] ) ; i f ( checkcoor ( input, order ) < 0){ return 1; return 1 ; void r o t a t e ( int n, int x, int y, int rx, int ry ) { i f ( ry == 0) { i f ( rx == 1) { x = n 1 x ; y = n 1 y ; int t = x ; x = y ; y = t ; void i h o r d e r ( int n, int d, int x, int y ) { int rx, ry, s, t=d ; x = y = 0 ; for ( s =1; s<n ; s =2) { rx = 1 & ( t / 2 ) ; ry = 1 & ( t ˆ rx ) ; r o t a t e ( s, x, y, rx, ry ) ; x += s rx ; y += s ry ; 12 t /= 4 ;

13 Solution: hmirror2.c #include horder. h #include u t i l. h int main ( int argc, char argv ) { i f ( validargs ( argc, argv )!= 1) { p r i n t f ( Argument e r r o r \n ) ; return 0 ; int x, y ; int input, order, max, mirror ; order = a t o i ( argv [ 2 ] ) ; input = a t o i ( argv [ 4 ] ) ; max = ( int )pow (2, order 2 ) ; mirror = (max 1) input ; i h o r d e r (1<<order, mirror, &x, &y ) ; p r i n t f ( %d %d\n, x, y ) ; return 0 ; Solution: hplot.sh #! / bin / bash input=$1 outputfile= hpoint. dat max=$ ( ( 2 ( input 2) 1)) rm ${ outputfile for i in seq 0 1 ${max ; do # echo e $ i. / hmirror2 n ${ input i $ i >> ${ outputfile done 13

14 Figure 4: Solution to the h-curve of order 6 (64 * 64 grid) and dimension 2 Q4 R-Tree [30 pts] Print answers on separate page, with [course-id] [hw#] [question#] [andrew-id] [your name] Grading info: graded by Zhoucheng Li Problem Description: The goal is to become familiar with the R-Tree algorithm. Your task is to add new functionality to the provided R-Tree package, called DRTREE 1. The package is in the./q4 directory of the provided tar-file package. Build the R-Tree package with tar -xvf christos-hw2.tar.gz; cd Q4/DRTree; make demo This creates the bin/drmain program. Run it on some small datasets and have some fun! It has been tested on the Unix/linux platform on the andrew machines - it should also run under mac-osx, and probably under Cygwin on Windows. Running make hw2 should load the appropriate dataset, and print the Implement me message. Currently the R-tree package supports s for range search, i for insertion and so on; use the -h flag, to list all the options. Implementation Details: You are required to implement the command t: 1 FYI, D stands for deferred split R-tree - but you don t need to worry about that. t 14

15 for intersection-join, using the input dataset input.hw2 (which is invoked by default with make hw2). This is a special case of the spatial join that we mentioned in class. Your code should work for any dimensionality d (d = 1, 2, 3,... ). The goal of this functionality is to return all pairs of overlapping data rectangles (one pair per line), and their count. Hint: Do explore the range query functions in the code package. Modify or follow the code to implement your own functionality. For the final results, run make spotless before you run make hw2 to clear the index file. With respect to the definition of overlap, re-use the function DRrectOverlap(), that is already in the DRTREE package. Of course, you should test your code for higher (and lower) dimensions, for corner cases (eg., empty tree), etc. Input Format: A line with just t should return all the pairs of intersecting rectangles, and the count N of such pairs. Do not report self-pairs and mirror pairs. That is, if rectangle R1 intersects rectangle R2, report only (R1, R2), omitting (R1, R1), (R2,R1) and (R2,R2). Output Format: Your program should print the total number N of qualifying pairs on the first (or last) line, and then, N lines, one for each pair of qualifying data rectangles (record number)) in tab-separated (tsv) format. Remember to omit self-pairs and mirror pairs. What to turn in: Code: [20 pts] In the provided tar-file package, work in the directory./q4 and implement the specified functionality. We will grade it using the commands: tar -xvfz yourandewid-hw2.tar.gz; cd Q4/DRTREE; make hw2 That is, typing in make hw2, we should produce your answers. We will also test on additional secret datasets, which we ll publish with the rest of the solutions. Grading info: -1 if handin format is not yourandewid-hw2.tar.gz -5 if code is not attached -5 if code fails to pass secret test -5 if code has minor bugs (e.g. the result is close to expected value) -10 if code has major bugs (e.g. the result drifts from expected value too much) Answers: [10 pts] On hard copy, submit 15

16 1. the function(s) you wrote (not the whole package), and 2. Only the number N of output lines (i.e., the count of qualifying pairs) when running make hw2. Grading info: - 5 if the result is close to expected value -10 if the result is far away from expected value (e.g 390, ,.. etc) Solution: Number of output lines: Code: refer to the tar file. 16