The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
Space and Time Hierarchies for Classes of Control Structures and Data Structures
Journal of the ACM (JACM)
Symbol manipulation by threaded lists
Communications of the ACM
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Managing storage for extendible arrays (Extended Abstract)
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
Optimal simulations between mesh-connected arrays of processors
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Optimal simulations between mesh-connected arrays of processors
Journal of the ACM (JACM)
Blocking for external graph searching
PODS '93 Proceedings of the twelfth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
On Embedding Between 2D Meshes of the Same Size
IEEE Transactions on Computers
Encoding Data Structures in Trees
Journal of the ACM (JACM)
Space-Time Trade-Offs in Structured Programming: An Improved Combinatorial Embedding Theorem
Journal of the ACM (JACM)
The Quadtree and Related Hierarchical Data Structures
ACM Computing Surveys (CSUR)
Probabilistic simulations (Preliminary Version)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Graphs that are almost binary trees (Preliminary Version)
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
Storage representations for tree-like data structures
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Object-based and image-based object representations
ACM Computing Surveys (CSUR)
On Embedding Rectangular Grids in Square Grids
IEEE Transactions on Computers
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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.