How close can an efficiently found solution come to the optimum?
8 records · Includes focused interests · How we rate progress
OpenAI reports randomized k-server competitive ratio O(log²(k+1)) on every metric against oblivious requests, matching the stated worst-case lower-bound order; distinct initial server positions need no additive term.
Read original source Original manuscript: claim, hypotheses, and contextgithub.com
Original report: 2026-10-06Coester, Koutsoupias and Zbysiński report that the work function algorithm is k-competitive on every metric space.
Original report: 2026-09-14The artifact reports (3,4,5,20,22,36) schedulable but (3,4,5,20,22,32) unschedulable, refuting the proposed six-task kernel cap.
Read original source Original researchgithub.com
Original report: 2026-09-30Becker, Greger and Peters report that every approval-based multiwinner election has a core committee and that one can be found in polynomial time.
Original report: 2026-09-10Kerger reports Ω(d²/log(d+1)) exact-function-value queries at accuracy Θ(d^−1/2) for deterministic convex Lipschitz minimization over a d-dimensional ball.
Original report: 2026-07-14The manuscript reports arbitrarily large additive configuration-LP gaps and additive-approximation hardness for rational item sizes greater than 1/6.
Read original source Original manuscript · family 118github.com
Original report: 2026-10-06The manuscript reports a deterministic polynomial-time algorithm producing a common superstring of length at most twice optimum.
Read original source Original manuscript · family 128github.com
Original report: 2026-10-06The authors report packing heuristics that outperform tested baselines on their online one-dimensional bin-packing experiments.
Original report: 2023-12-14How close can an efficiently found solution come to the optimum? We distinguish additive and multiplicative guarantees, fractional relaxations, worst-case theorems, and instance-specific experiments.
This topic groups related mathematical questions across publishers. Each focused problem carries its own baseline and each contribution retains its original source. Results are compared only when their assumptions, optimization target, and computation model agree.
Background review: 2026-10-11. Selected sources:
Publication dates and editorial changes.
AI-assisted core existence in approval-based committee elections
AI-assisted near-quadratic lower bound for exact-value optimization
OpenAI reports: Configuration-LP gaps in offline bin packing
OpenAI reports: Configuration-LP gaps in offline bin packing
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