Preserving Average Proximity in Arrays

Programmers and data structure designers are often
forced to choose between alternative structures. 
 In storing these structures, preserving logical adjacencies
or "proximity" is usually an important consideration. 
 The combinatorial problem of storing arrays as various
kinds of list structures is examined.  Embeddings 
of graphs are used to model the loss of proximity involved
in such storage schemes, and an elementary 
proof that arrays cannot be stored as linear lists with
bounded loss of proximity is presented.  Average 
loss of proximity is then considered, and it is shown
that arrays cannot be stored as linear lists with 
only bounded loss of average proximity, but can be so
stored in binary trees.  The former result implies, 
for instance, that row major order is an asymptotically
optimal storage strategy for arrays.

CACM March, 1978

DeMillo, R.
Eisenstat, S.
Lipton, R.

arrays, graph embedding, linear lists,
proximity, average proximity, trees

4.34 5.24 5.25 5.32

CA780305 JB March 28, 1978  1:07 PM

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