PPL 115 / 177 permanent IDsPrize Problem Ledger · PPLChecked 2026.07.27
Prize Problem LedgerNanongkai Open €PPL 115Nanongkai · Cut-query reachability

Permanent problem IDPPL 115

Verified openIndependentconjecture

Algorithms

Nanongkai · Cut-query reachability

Given a hidden directed unweighted graph where cut(S) returns the number of edges leaving S, either give an O(|V|^1.999)-query algorithm for s–t reachability or rule out O(|V|^1.001) queries; a smaller sub-bounty asks for any improvement below O(|V|²/log n).

graph queriesreachabilityquery complexity
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The problem

Given a hidden directed unweighted graph where cut(S) returns the number of edges leaving S, either give an O(|V|^1.999)-query algorithm for s–t reachability or rule out O(|V|^1.001) queries; a smaller sub-bounty asks for any improvement below O(|V|²/log n).

Open since2024reward first offered
Last checked2026.07.27Catalog verification
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Reward offers

Offer 01€110 main targetDanupon Nanongkai
Personal offer

The official page reserves each cash prize for the first solver. Resolve either side of the main query-complexity target. The current listing expires in 2034.

Published deadline: 2034-12-31

Offer 02€5 improvement targetDanupon Nanongkai
Personal offer

Improve the O(|V|²/log n) cut-query upper bound, for example to O(|V|²/(log n log log n)). This is a sub-bounty attached to the same reachability problem.

Published deadline: 2034-12-31

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Sources & reading