STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Succinct indexable dictionaries with applications to encoding k-ary trees and multisets
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Low Redundancy in Static Dictionaries with Constant Query Time
SIAM Journal on Computing
Succinct Representation of Balanced Parentheses and Static Trees
SIAM Journal on Computing
High-order entropy-compressed text indexes
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the 16th Conference on Foundations of Software Technology and Theoretical Computer Science
Succinct representation of balanced parentheses, static trees and planar graphs
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Fast Compression with a Static Model in High-Order Entropy
DCC '04 Proceedings of the Conference on Data Compression
When indexing equals compression: experiments with compressing suffix arrays and applications
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
The level ancestor problem simplified
Theoretical Computer Science - Latin American theorotical informatics
Compact oracles for reachability and approximate distances in planar digraphs
Journal of the ACM (JACM)
Structuring labeled trees for optimal succinctness, and beyond
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Representing Trees of Higher Degree
Algorithmica
Ramsey partitions and proximity data structures
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
ACM Computing Surveys (CSUR)
Note: A simple storage scheme for strings achieving entropy bounds
Theoretical Computer Science
Ultra-succinct representation of ordered trees
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Succinct indexes for strings, binary relations and multi-labeled trees
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Compressed data structures: Dictionaries and data-aware measures
Theoretical Computer Science
Rank and select revisited and extended
Theoretical Computer Science
On searching compressed string collections cache-obliviously
Proceedings of the twenty-seventh ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Space-efficient static trees and graphs
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
| Hi-index | 5.23 |
Let G be an unweighted and undirected graph of n nodes, and let D be the nxn matrix storing the All-Pairs-Shortest-Path Distances in G. Since D contains integers in [n]@?+~, its plain storage takes n^2log(n+1) bits. However, a simple counting argument shows that n^2/2 bits are necessary to store D. In this paper we investigate the question of finding a succinct representation of D that requires O(n^2) bits of storage and still supports constant-time access to each of its entries. This is asymptotically optimal in the worst case, and far from the information-theoretic lower bound by a multiplicative factor log"23~1.585. As a result O(1) bits per pairs of nodes in G are enough to retain constant-time access to their shortest-path distance. We achieve this result by reducing the storage of D to the succinct storage of labeled trees and ternary sequences, for which we properly adapt and orchestrate the use of known compressed data structures. This approach can be easily and optimally extended to graphs whose edge weights are positive integers bounded by a constant value.