Pith Number

pith:QCKY74JW

pith:2026:QCKY74JWBIX3LDQYNN343XVIV5

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Partial Optimality in the Preordering Problem

Bjoern Andres, David Stein, Jannik Irmai

New partial optimality conditions decide more pairs that cannot appear in any optimal preorder.

arxiv:2602.17346 v2 · 2026-02-19 · cs.DM · cs.DS · cs.LG

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Record completeness

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Claims

C1strongest claim

Building on the state of the art in solving this NP-hard problem partially, we contribute new partial optimality conditions and efficient algorithms for deciding these conditions. In experiments with real and synthetic data, these new conditions increase, in particular, the fraction of pairs ab for which it is decided efficiently that a ≰ b in an optimal preorder.

C2weakest assumption

The new conditions are valid partial optimality conditions that correctly identify pairs that cannot be related in any optimal preorder, and the algorithms correctly decide them without false negatives.

C3one line summary

New partial optimality conditions for the preordering problem increase the fraction of pairs decidable as unrelated in an optimal preorder.

References

13 extracted · 13 resolved · 0 Pith anchors

[1] Jacob, J., Jentsch, M., Kostka, D., Bentink, S., and Spang, R 2008 · doi:10.1093/bioinformatics/btn056

[2] doi: 10.11606/resimeusp.v3i3.74876. Weller, M., Komusiewicz, C., Niedermeier, R., and Uhlmann, J. On making directed graphs transitive. Jour- nal of Computer and System Sciences , 78(2):559–574, · doi:10.11606/resimeusp.v3i3.74876

[3] 9 Partial Optimality in the Preordering Problem A 2011 · doi:10.1016/j.jcss.2011.07.001

[4] 6.2 is fulfilled for every ij ∈ δ(U, V \ U) as c− ij ≥ X pq∈δ(U,V \U )\ˆx−1(0) c+ pq = 0

[5] Since γij|1(x)ij = 1 for all x ∈ XV [ˆx], there is an optimal solu- tion x∗ to POPV,c[ˆx] such that x∗ ij = 1

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T02:44:31.121163Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

80958ff1360a2fb58e186b77cddea8af78558d4938622af9c572f0f6212527c1

Aliases

arxiv: 2602.17346 · arxiv_version: 2602.17346v2 · doi: 10.48550/arxiv.2602.17346 · pith_short_12: QCKY74JWBIX3 · pith_short_16: QCKY74JWBIX3LDQY · pith_short_8: QCKY74JW

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/QCKY74JWBIX3LDQYNN343XVIV5 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 80958ff1360a2fb58e186b77cddea8af78558d4938622af9c572f0f6212527c1

Canonical record JSON

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      "cs.LG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2026-02-19T13:29:09Z",
    "title_canon_sha256": "695a92b78e77fc37f9ef05d8ddb2e12edb48a7b5ea86df176d7b57860370d08f"
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