Pith Number

pith:BYPZSAE3

pith:2026:BYPZSAE3CU5SLNJMQTWH4TJXXN

not attested not anchored not stored refs pending

Min-Sum Set Cover on Parallel Machines

Micha{\l} Szyfelbein

A bicriteria LP-based algorithm for parallel maximum coverage yields O(log m / log log m) approximations for min-sum set cover on unrelated machines and a constant-factor guarantee on related machines.

arxiv:2604.11388 v3 · 2026-04-13 · cs.DS

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BYPZSAE3CU5SLNJMQTWH4TJXXN}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We give a randomized bicriteria (1-1/e-ε, O(log m/log log m))-approximation algorithm for Parallel Maximum Coverage based on a natural LP relaxation. This can be then used to obtain O(log m/log log m)-approximation algorithm for the Min-Sum Set Cover problem on unrelated machines. For related machines we obtain an 8e/(e+1)+ε <12.66-approximation.

C2weakest assumption

That the stated bicriteria approximation for the Parallel Maximum Coverage subproblem holds via the LP relaxation and can be leveraged without additional hidden factors that would invalidate the derived ratios for the main Min-Sum Set Cover problems.

C3one line summary

Approximation algorithms are given for the Parallel Min-Sum Set Cover problem, including a bicriteria (1-1/e-ε, O(log m/log log m)) result for a key subproblem leading to O(log m/log log m) for unrelated machines and <12.66 for related machines.

Receipt and verification

First computed	2026-05-29T02:05:44.801361Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0e1f99009b153b25b52c84ec7e4d37bb5a57d2bbb6e07331065ca51c5a7dc75e

Aliases

arxiv: 2604.11388 · arxiv_version: 2604.11388v3 · doi: 10.48550/arxiv.2604.11388 · pith_short_12: BYPZSAE3CU5S · pith_short_16: BYPZSAE3CU5SLNJM · pith_short_8: BYPZSAE3

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BYPZSAE3CU5SLNJMQTWH4TJXXN \
  | 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: 0e1f99009b153b25b52c84ec7e4d37bb5a57d2bbb6e07331065ca51c5a7dc75e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c41034e05e6ae66a74fa7bcc7c52c9be99f0b0ff07ae8beb7c4e4b5c287c794e",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2026-04-13T12:29:05Z",
    "title_canon_sha256": "794a273f10e90dc9b788a0b58d5d096ec6d50fe6deb4ae9dcdd8795fa84b1878"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.11388",
    "kind": "arxiv",
    "version": 3
  }
}