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Fix #90: Add ClosestVectorProblem model #92

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Merged
GiggleLiu merged 10 commits into from
Feb 28, 2026
Merged

Fix #90: Add ClosestVectorProblem model #92

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00ce084
Add plan for #90: ClosestVectorProblem model
GiggleLiu Feb 22, 2026
41d4963
Merge branch 'main' into issue-90-closest-vector-problem
GiggleLiu Feb 28, 2026
ec23ad8
Merge branch 'main' into issue-90-closest-vector-problem
GiggleLiu Feb 28, 2026
b720481
docs: update CVP plan for refactored variant system and Copilot review
GiggleLiu Feb 28, 2026
0c534dd
Merge branch 'main' into issue-90-closest-vector-problem
GiggleLiu Feb 28, 2026
9827a1e
feat: add ClosestVectorProblem model (#90)
GiggleLiu Feb 28, 2026
c6dc4b9
chore: remove completed CVP implementation plan
GiggleLiu Feb 28, 2026
407f7b3
fix: improve CVP paper entry and add missing citations
GiggleLiu Feb 28, 2026
5481e29
save
GiggleLiu Feb 28, 2026
1d7372e
chore: add Typst drawing rule for CeTZ conventions
GiggleLiu Feb 28, 2026
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9 changes: 9 additions & 0 deletions docs/paper/reductions.typ
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Expand Up @@ -50,6 +50,7 @@
"PaintShop": [Paint Shop],
"BicliqueCover": [Biclique Cover],
"BinPacking": [Bin Packing],
"ClosestVectorProblem": [Closest Vector Problem],
)

// Definition label: "def:<ProblemName>" — each definition block must have a matching label
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) <fig:ilp-example>
]

#problem-def("ClosestVectorProblem")[
Given a lattice basis $bold(B) in RR^(m times n)$ (columns $bold(b)_1, dots, bold(b)_n in RR^m$ spanning lattice $cal(L)(bold(B)) = {bold(B) bold(x) : bold(x) in ZZ^n}$) and target $bold(t) in RR^m$, find $bold(x) in ZZ^n$ minimizing $norm(bold(B) bold(x) - bold(t))_2$.
][
The Closest Vector Problem is a fundamental lattice problem, proven NP-hard by van Emde Boas @vanemde1981. CVP plays a central role in lattice-based cryptography and the geometry of numbers. Kannan's algorithm @kannan1987 solves CVP in $O^*(n^n)$ time using the Hermite normal form, later improved to $O^*(2^n)$ via the randomized sieve of Micciancio and Voulgaris @micciancio2010. CVP is closely related to the Shortest Vector Problem (SVP) and integer programming: Lenstra's algorithm for fixed-dimensional ILP @lenstra1983 proceeds via CVP in the dual lattice.
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Copilot AI Feb 28, 2026

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The new CVP definition introduces citation keys @vanemde1981, @kannan1987, and @micciancio2010, but these keys do not appear in docs/paper/references.bib. This will likely result in unresolved citations (and may fail the paper build, depending on CI settings). Add the missing BibTeX entries or change the citation keys to ones that already exist in the bibliography.

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The Closest Vector Problem is a fundamental lattice problem, proven NP-hard by van Emde Boas @vanemde1981. CVP plays a central role in lattice-based cryptography and the geometry of numbers. Kannan's algorithm @kannan1987 solves CVP in $O^*(n^n)$ time using the Hermite normal form, later improved to $O^*(2^n)$ via the randomized sieve of Micciancio and Voulgaris @micciancio2010. CVP is closely related to the Shortest Vector Problem (SVP) and integer programming: Lenstra's algorithm for fixed-dimensional ILP @lenstra1983 proceeds via CVP in the dual lattice.
The Closest Vector Problem is a fundamental lattice problem, proven NP-hard by van Emde Boas (1981). CVP plays a central role in lattice-based cryptography and the geometry of numbers. Kannan's algorithm (1987) solves CVP in $O^*(n^n)$ time using the Hermite normal form, later improved to $O^*(2^n)$ via the randomized sieve of Micciancio and Voulgaris (2010). CVP is closely related to the Shortest Vector Problem (SVP) and integer programming: Lenstra's algorithm for fixed-dimensional ILP @lenstra1983 proceeds via CVP in the dual lattice.

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*Example.* Consider the 2D lattice with basis $bold(b)_1 = (2, 0)^top$, $bold(b)_2 = (1, 2)^top$ and target $bold(t) = (2.8, 1.5)^top$. The lattice points near $bold(t)$ include $bold(B)(1, 0)^top = (2, 0)^top$, $bold(B)(1, 1)^top = (3, 2)^top$, and $bold(B)(0, 1)^top = (1, 2)^top$. The closest is $bold(B)(1, 1)^top = (3, 2)^top$ with distance $norm((0.2, 0.5))_2 approx 0.539$.
]

== Satisfiability Problems

#problem-def("Satisfiability")[
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