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OP-11903Status unassessedGraph theory

Single-exponential algorithms parameterized by clique-width

Single-exponential algorithms parameterized by clique-width. Current research status is unassessed. The dated source poses this question; inclusion does not certify that it remains open today.

MSC 05C · Graph theoryMSC 68Q25 · Analysis of algorithms and problem complexity

Editorial MSC2020 mapping of Single-exponential algorithms parameterized by clique-width. https://drops.dagstuhl.de/storage/04dagstuhl-reports/volume15/issue01/25041/DagRep.15.1.105/DagRep.15.1.105.pdf#page=14 Not an author-supplied code.

Source question · editorial summaryAs of 2025; current status unassessedSource & evidence ↓
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Problem statement

For standard problems admitting 2O(k)nO(1)2^{O(k)}n^{O(1)} algorithms when a clique-width-kk expression is supplied, can this running time be attained from the graph alone, parameterized by its clique-width kk? Section 4.6 contrasts this with the known 2O(klog⁡k)2^{O(k\log k)} approach.

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Editorial question summary. Consult the linked source for the complete model, assumptions and discussion.

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Current research status is unassessed. The dated source poses this question; inclusion does not certify that it remains open today.

References
  1. [1]Seminar 25041 problem-session contributors. Dagstuhl 25041 — Graph Classes and Algorithmic Complexity (2025).; Single-exponential algorithms parameterized by clique-width linkCC BY 4.0; attributed editorial adaptation of the named section authors.

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