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Efficient Storage of Sparse Matrices Using Circular Linked Lists

Learn about the benefits of circular linked lists for storing sparse matrices with a large number of zero elements, reducing wasted space in memory. Discover the data structures and implementation techniques for efficient matrix representation.

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Efficient Storage of Sparse Matrices Using Circular Linked Lists

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  1. Department of Computer and Information Science,School of Science, IUPUI CSCI 240 Abstract Data Types Sparse Matrices Dale Roberts, Lecturer IUPUI droberts@cs.iupui.edu

  2. Sparse Matrices é ù 0 0 11 0 ê ú 12 5 0 0 ê ú - ê ú 0 4 0 0 ê ú - 0 0 0 15 ë û Sparse matrices have a large number of zero elements in proportion to the number of nonzero elements. Storing in n x n array will have a lot of wasted space. Alternative: circular lists storing only nonzero elements.

  3. down head right next row col down entry right value Sparse Matrix Nodes # of head nodes = # of rows + # of columns head node entry node tag j i aij aij tag is used to tell entry, head and aij nodes part

  4. Linked Representation for Matrix 4 4 0 2 11 1 1 1 0 12 5 1 2 -4 3 3 -15 Circular linked list

  5. Sparse Matrix Data Structure #define MAX_SIZE 50 /* size of largest matrix */typedef enum {head, entry} tagfield;typedef struct matrix_node *matrix_pointer;typedef struct entry_node { int row; int col; int value; };typedef struct matrix_node { matrix_pointer down; matrix_pointer right; tagfield tag; union { matrix_pointer next; entry_node entry; } u; };matrix_pointer hdnode[MAX_SIZE];

  6. Try creating your data for this matrix

  7. Acknowledgements • All of this code is from Horowitz, Sahni, and Anderson-Freed, Fundamentals of Data Structures in C. • Some slides were originally developed by Chen, Hsin-His.

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