What is recorded here?
The paper constructed static sparse-set representations with constant worst-case membership query time and linear space, then refined word storage to n plus a sublinear remainder under its stated model. Ordinary hashing can be fast on average while leaving unlucky queries expensive. Fredman, Komlós and Szemerédi fixed the set in advance and used two levels of placement. A first hash is chosen so the sum of squared bucket sizes stays small. Each bucket then gets enough space for a second hash with no collisions among its stored keys. A query follows a constant number of table probes and compares the stored key with the requested key; reaching an occupied position alone does not prove membership. The paper also separates finding the representation from using it: constant worst-case query time does not imply constant insertion time. A refinement packs auxiliary tables so total storage approaches one universe-sized word per stored item. This is a static dictionary result in a specified word/probe model. Dynamic updates, arbitrary-length key costs, modern succinct bit bounds and production-system behavior are separate questions.
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Scientific scope
The result concerns a static key set and the specified word-RAM/hash-family assumptions. Randomized construction can produce linear-space storage with worst-case constant lookup, but construction and lookup guarantees are different. It does not provide unrestricted dynamic updates, adversarial chosen-key security or free computation on arbitrarily long keys. Implementation constants and practical throughput have not been replayed.
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- Fredman, Komlós and Szemerédi: static sparse tables with constant worst-case lookup — exact original scientific paper
- Fredman, Komlós and Szemerédi: static sparse tables with constant worst-case lookup — publisher deposit
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People and systems
Michael L. Fredman; János Komlós; Endre Szemerédi
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English catalogue narrative
Fredman, Komlós and Szemerédi: static sparse tables with constant worst-case lookup
The paper constructed static sparse-set representations with constant worst-case membership query time and linear space, then refined word storage to n plus a sublinear remainder under its stated model.
Ordinary hashing can be fast on average while leaving unlucky queries expensive. Fredman, Komlós and Szemerédi fixed the set in advance and used two levels of placement. A first hash is chosen so the sum of squared bucket sizes stays small. Each bucket then gets enough space for a second hash with no collisions among its stored keys. A query follows a constant number of table probes and compares the stored key with the requested key; reaching an occupied position alone does not prove membership. The paper also separates finding the representation from using it: constant worst-case query time does not imply constant insertion time. A refinement packs auxiliary tables so total storage approaches one universe-sized word per stored item. This is a static dictionary result in a specified word/probe model. Dynamic updates, arbitrary-length key costs, modern succinct bit bounds and production-system behavior are separate questions.
Scientific scope
The result concerns a static key set and the specified word-RAM/hash-family assumptions. Randomized construction can produce linear-space storage with worst-case constant lookup, but construction and lookup guarantees are different. It does not provide unrestricted dynamic updates, adversarial chosen-key security or free computation on arbitrarily long keys. Implementation constants and practical throughput have not been replayed.
People and systems
Michael L. Fredman; János Komlós; Endre Szemerédi