diff --git a/ROADMAP.md b/ROADMAP.md index 5e692408e6..710bf7d823 100644 --- a/ROADMAP.md +++ b/ROADMAP.md @@ -202,7 +202,7 @@ index links to canonical definitions rather than keeping a second set. - **Reducibilities** ([#1351]): logspace Turing reductions, in an oracle model whose query tape is not charged to the space bound, and their transitivity; the rest of the inclusion hierarchy of Ladner, Lynch and Selman, and its separations. -- **Sparse and tally sets** ([#1819]): `P/poly = P^SPARSE` (Meyer), extending +- **Sparse and tally sets:** `P/poly = P^SPARSE` (Meyer), extending `PPoly.of_sparse` in `Circuit/Boolean/Sparse.lean`. - **Berman–Hartmanis:** p-isomorphism and paddability; paddable NP-complete sets are p-isomorphic, so the standard NP-complete problems are all p-isomorphic to SAT; the isomorphism conjecture as a @@ -503,17 +503,15 @@ reusing graph and matroid foundations and the shared data-structure interfaces. - **Spanning trees and matroids:** minimum spanning trees with sorting and disjoint-set costs; weighted matroid greedy optimality with an independence-oracle interface; then matroid intersection with explicit oracle and implementation costs. -- **Submodular optimization:** the `1 - 1/e` approximation for nonnegative monotone submodular - maximization under a cardinality constraint, charging value-oracle calls separately from their - concrete realizations; then further constraints and approximation bounds. +- **Submodular optimization:** further constraints and approximation bounds beyond the + cardinality-constrained `1 - 1/e` greedy, charging value-oracle calls separately from their + concrete realizations. ### Online algorithms and competitive analysis - Request sequences, online strategies, offline optima and competitive ratios with additive constants; distinguish deterministic and randomized strategies and oblivious and adaptive adversaries. Compare algorithms in the same action and cost model, including initialization. -- **Paging:** an LRU competitive bound and a matching deterministic lower bound as the first - clients. Reuse native amortized certificates and make adversarial request generation explicit. - **Adaptive search trees:** a BST access-and-rotation model, the splay access lemma, static optimality, working-set and dynamic-finger bounds, and Wilber-style lower bounds. State dynamic optimality as a conjectural research target with explicit strategy and sequence quantifiers. @@ -868,5 +866,4 @@ not planned, not as proved. [#1524]: https://github.com/cslib-community/complexitylib/issues/1524 [#1572]: https://github.com/cslib-community/complexitylib/issues/1572 [#1817]: https://github.com/cslib-community/complexitylib/issues/1817 -[#1819]: https://github.com/cslib-community/complexitylib/issues/1819 [#1824]: https://github.com/cslib-community/complexitylib/issues/1824