Question

I have the following C code from here:

http://marknelson.us/1989/10/01/lzw-data-compression/

It states that it uses a XOR hashing algorithm to avoid having to search through substring array elements and instead generate an “address” for a substring.

Then there is a hashing function, for which the line below seems to me as being the main part:

index = (hash_character << HASHING_SHIFT) ^ hash_prefix;

• Here we have an integer value that is shifted ranging from 4 bits to the left (according to definitions of constants).

• Then this value gets an XOR applied with another integer value.

I am pretty sure that the shifting part is just to get rid of unused bits, and then a single, simple XOR operation is being applied to a very short substring, from 12 to 16 bits; although I might be very wrong on this.

What is the name, or possible list of algorithm names, that explain this specific XOR hashing algorithm, or if possible, a list of algorithm names that are good for this substring application (like in the LZW dictionary of substrings, etc.)?

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#define BITS 12                   /* Setting the number of bits to 12, 13*/
#define HASHING_SHIFT (BITS-8)    /* or 14 affects several constants.    */
#define MAX_VALUE (1 << BITS) - 1 /* Note that MS-DOS machines need to   */
#define MAX_CODE MAX_VALUE - 1    /* compile their code in large model if*/
                                  /* 14 bits are selected.               */
#if BITS == 14
  #define TABLE_SIZE 18041        /* The string table size needs to be a */
#endif                            /* prime number that is somewhat larger*/
#if BITS == 13                    /* than 2**BITS.                       */
  #define TABLE_SIZE 9029
#endif
#if BITS <= 12
  #define TABLE_SIZE 5021
#endif

……

……

……

/*
** This is the hashing routine.  It tries to find a match for the prefix+char
** string in the string table.  If it finds it, the index is returned.  If
** the string is not found, the first available index in the string table is
** returned instead.
*/

int find_match(int hash_prefix,unsigned int hash_character)
{
int index;
int offset;

  index = (hash_character << HASHING_SHIFT) ^ hash_prefix;
  if (index == 0)
    offset = 1;
  else
    offset = TABLE_SIZE - index;
  while (1)
  {
    if (code_value[index] == -1)
      return(index);
    if (prefix_code[index] == hash_prefix &&
        append_character[index] == hash_character)
      return(index);
    index -= offset;
    if (index < 0)
      index += TABLE_SIZE;
  }
}

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Answer 1

A similar hash function was described in Bruno Preiss’ “Data Structures and Algorithms with Object-Oriented Design Patterns in Java” John Wiley & Sons, 2000

A nice – but somewhat outdated – survey of hash function is here. The function is named “BPhash” in the survey. The LZW hash function looks very simple to me. There are probably better hash function known by now which produce less fequent clashes und thus improve the hashing efficiency/effectiveness.