QCSP on partially reflexive cycles - the wavy line of tractability
Florent Madelaine, Barnaby Martin
TL;DR
This paper establishes a complexity dichotomy for the QCSP on partially reflexive cycles, showing it is either solvable in NL or NP-hard, with the boundary characterized by intricate conditions.
Contribution
It provides a novel complexity classification for QCSP on partially reflexive cycles, revealing a nuanced boundary between tractable and hard cases.
Findings
QCSP(H) is either in NL or NP-hard for partially reflexive cycles
The boundary between tractability and hardness is characterized by complex conditions
The results form a 'wavy line' of tractability in the complexity landscape
Abstract
We study the (non-uniform) quantified constraint satisfaction problem QCSP(H) as H ranges over partially reflexive cycles. We obtain a complexity-theoretic dichotomy: QCSP(H) is either in NL or is NP-hard. The separating conditions are somewhat esoteric hence the epithet "wavy line of tractability".
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Taxonomy
TopicsAdvanced Graph Theory Research · Constraint Satisfaction and Optimization · Complexity and Algorithms in Graphs