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Fix #445: [Model] AdditionalKey (#681)
* Add plan for #445: [Model] AdditionalKey * Implement AdditionalKey satisfaction problem model (#445) Add the Additional Key problem from relational database theory (Garey & Johnson SR7). Given a relational schema (R, F) and known candidate keys K, determines whether R has a candidate key not in K. - Model file with closure computation, minimality check, and known-key filter - 13 unit tests covering creation, evaluation, edge cases, brute force, serialization - CLI create support with --num-attributes, --dependencies, --relation-attrs, --known-keys - Module registration and re-exports - Canonical example-db entry with regenerated fixtures Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com> * Apply rustfmt formatting fixes Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com> * Add AdditionalKey model (Batch 1) Implement the AdditionalKey satisfaction problem from relational database theory (Garey & Johnson A4 SR27). Includes model, CLI registration, unit tests, and example-db entry. * Add AdditionalKey problem definition to paper Add problem-def entry, display name, and bibliography reference (Beeri & Bernstein, 1979) for the Additional Key problem from relational database theory. Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com> * chore: remove plan file after implementation * Fix AdditionalKey canonical example to use updated ModelExampleSpec API The merge brought in API changes to ModelExampleSpec (removed `build` closure, added direct `instance`/`optimal_config`/`optimal_value` fields). Update AdditionalKey's canonical_model_example_specs to match. Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com> * Address review findings: panic tests, pinned solution count, help text - Add 5 #[should_panic] tests for constructor validation paths - Pin brute-force solution count to 2 (additional keys: {0,2} and {0,3,5}) - Fix --known-keys help text to use [brackets] for optional flag - Remove redundant test_additional_key_paper_example Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com> * Fix merge artifacts: fmt, missing fields in test helper Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com> * Cover data getter methods in creation test Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com> --------- Co-authored-by: Claude Opus 4.6 <noreply@anthropic.com> Co-authored-by: Xiwei Pan <xiwei.pan@connect.hkust-gz.edu.cn>
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‎docs/paper/reductions.typ‎

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@@ -62,6 +62,7 @@
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// Problem display names for theorem headers
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#let display-name = (
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"AdditionalKey": [Additional Key],
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"MaximumIndependentSet": [Maximum Independent Set],
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"MinimumVertexCover": [Minimum Vertex Cover],
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"MaxCut": [Max-Cut],
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) <fig:d2cif>
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]
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#problem-def("AdditionalKey")[
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Given a set $A$ of attribute names, a collection $F$ of functional dependencies on $A$,
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a subset $R subset.eq A$, and a set $K$ of candidate keys for the relational scheme $chevron.l R, F chevron.r$,
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determine whether there exists a subset $R' subset.eq R$ such that $R' in.not K$,
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the closure $R'^+$ under $F$ equals $R$, and no proper subset of $R'$ also has this property.
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][
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A classical NP-complete problem from relational database theory @beeri1979.
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Enumerating all candidate keys is necessary to verify Boyce-Codd Normal Form (BCNF),
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and the NP-completeness of Additional Key implies that BCNF testing is intractable in general.
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The best known exact algorithm is brute-force enumeration of all $2^(|R|)$ subsets,
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checking each for the key property via closure computation under Armstrong's axioms.
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#footnote[No algorithm improving on brute-force is known for the Additional Key problem.]
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*Example.* Consider attribute set $A = {0, 1, 2, 3, 4, 5}$ with functional dependencies
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$F = {{0,1} -> {2,3}, {2,3} -> {4,5}, {4,5} -> {0,1}, {0,2} -> {3}, {3,5} -> {1}}$,
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relation $R = A$, and known keys $K = {{0,1}, {2,3}, {4,5}}$.
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The subset ${0,2}$ is an additional key: starting from ${0,2}$, we apply ${0,2} -> {3}$
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to get ${0,2,3}$, then ${2,3} -> {4,5}$ to get ${0,2,3,4,5}$, then ${4,5} -> {0,1}$
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to reach $R^+ = A$. The set ${0,2}$ is minimal (neither ${0}$ nor ${2}$ alone determines $A$)
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and ${0,2} in.not K$, so the answer is YES.
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]
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#{
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let x = load-model-example("ConjunctiveBooleanQuery")
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let d = x.instance.domain_size

‎docs/paper/references.bib‎

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@@ -198,6 +198,17 @@ @article{lucas2014
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year = {2014}
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}
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@article{beeri1979,
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author = {Catriel Beeri and Philip A. Bernstein},
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title = {Computational Problems Related to the Design of Normal Form Relational Schemas},
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journal = {ACM Transactions on Database Systems},
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volume = {4},
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number = {1},
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pages = {30--59},
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year = {1979},
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doi = {10.1145/320064.320066}
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}
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@article{barahona1982,
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author = {Francisco Barahona},
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title = {On the computational complexity of Ising spin glass models},

‎problemreductions-cli/src/cli.rs‎

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@@ -257,6 +257,7 @@ Flags by problem type:
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OptimalLinearArrangement --graph, --bound
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RuralPostman (RPP) --graph, --edge-weights, --required-edges, --bound
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MultipleChoiceBranching --arcs [--weights] --partition --bound [--num-vertices]
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AdditionalKey --num-attributes, --dependencies, --relation-attrs [--known-keys]
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SubgraphIsomorphism --graph (host), --pattern (pattern)
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LCS --strings, --bound [--alphabet-size]
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FAS --arcs [--weights] [--num-vertices]
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/// Alphabet size for LCS, SCS, or StringToStringCorrection (optional; inferred from the input strings if omitted)
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#[arg(long)]
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pub alphabet_size: Option<usize>,
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/// Number of attributes for AdditionalKey or MinimumCardinalityKey
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#[arg(long)]
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pub num_attributes: Option<usize>,
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/// Functional dependencies for AdditionalKey (e.g., "0,1:2,3;2,3:4,5") or MinimumCardinalityKey (semicolon-separated "lhs>rhs" pairs, e.g., "0,1>2;0,2>3")
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#[arg(long)]
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pub dependencies: Option<String>,
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/// Relation scheme attributes for AdditionalKey (comma-separated, e.g., "0,1,2,3,4,5")
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#[arg(long)]
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pub relation_attrs: Option<String>,
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/// Known candidate keys for AdditionalKey (e.g., "0,1;2,3")
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#[arg(long)]
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pub known_keys: Option<String>,
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/// Domain size for ConjunctiveBooleanQuery
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#[arg(long)]
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pub domain_size: Option<usize>,
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/// Number of groups for SumOfSquaresPartition
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#[arg(long)]
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pub num_groups: Option<usize>,
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/// Functional dependencies for MinimumCardinalityKey (semicolon-separated "lhs>rhs" pairs, e.g., "0,1>2;0,2>3")
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#[arg(long)]
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pub dependencies: Option<String>,
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/// Number of attributes for MinimumCardinalityKey
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#[arg(long)]
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pub num_attributes: Option<usize>,
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/// Source string for StringToStringCorrection (comma-separated symbol indices, e.g., "0,1,2,3")
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#[arg(long)]
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pub source_string: Option<String>,

‎problemreductions-cli/src/commands/create.rs‎

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@@ -14,7 +14,7 @@ use problemreductions::models::graph::{
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MultipleChoiceBranching, SteinerTree, StrongConnectivityAugmentation,
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};
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use problemreductions::models::misc::{
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BinPacking, BoyceCoddNormalFormViolation, CbqRelation, ConjunctiveBooleanQuery,
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AdditionalKey, BinPacking, BoyceCoddNormalFormViolation, CbqRelation, ConjunctiveBooleanQuery,
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FlowShopScheduling, LongestCommonSubsequence, MinimumTardinessSequencing,
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MultiprocessorScheduling, PaintShop, PartiallyOrderedKnapsack, QueryArg,
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RectilinearPictureCompression, ResourceConstrainedScheduling,
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&& args.sink_2.is_none()
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&& args.requirement_1.is_none()
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&& args.requirement_2.is_none()
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&& args.num_attributes.is_none()
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&& args.dependencies.is_none()
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&& args.relation_attrs.is_none()
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&& args.known_keys.is_none()
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&& args.domain_size.is_none()
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&& args.relations.is_none()
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&& args.conjuncts_spec.is_none()
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"MultipleChoiceBranching" => {
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"--arcs \"0>1,0>2,1>3,2>3,1>4,3>5,4>5,2>4\" --weights 3,2,4,1,2,3,1,3 --partition \"0,1;2,3;4,7;5,6\" --bound 10"
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}
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"AdditionalKey" => "--num-attributes 6 --dependencies \"0,1:2,3;2,3:4,5;4,5:0,1\" --relation-attrs 0,1,2,3,4,5 --known-keys \"0,1;2,3;4,5\"",
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"SubgraphIsomorphism" => "--graph 0-1,1-2,2-0 --pattern 0-1",
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"RectilinearPictureCompression" => {
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"--matrix \"1,1,0,0;1,1,0,0;0,0,1,1;0,0,1,1\" --k 2"
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}
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}
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// AdditionalKey
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"AdditionalKey" => {
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let usage = "Usage: pred create AdditionalKey --num-attributes 6 --dependencies \"0,1:2,3;2,3:4,5\" --relation-attrs \"0,1,2,3,4,5\" --known-keys \"0,1;2,3\"";
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let num_attributes = args.num_attributes.ok_or_else(|| {
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anyhow::anyhow!("AdditionalKey requires --num-attributes\n\n{usage}")
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})?;
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let deps_str = args.dependencies.as_deref().ok_or_else(|| {
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anyhow::anyhow!("AdditionalKey requires --dependencies\n\n{usage}")
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})?;
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let ra_str = args.relation_attrs.as_deref().ok_or_else(|| {
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anyhow::anyhow!("AdditionalKey requires --relation-attrs\n\n{usage}")
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})?;
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let dependencies: Vec<(Vec<usize>, Vec<usize>)> = deps_str
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.split(';')
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.map(|dep| {
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let parts: Vec<&str> = dep.trim().split(':').collect();
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anyhow::ensure!(
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parts.len() == 2,
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"Invalid dependency format '{}', expected 'lhs:rhs' (e.g., '0,1:2,3')",
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dep.trim()
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);
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let lhs: Vec<usize> = util::parse_comma_list(parts[0].trim())?;
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let rhs: Vec<usize> = util::parse_comma_list(parts[1].trim())?;
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Ok((lhs, rhs))
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})
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.collect::<Result<Vec<_>>>()?;
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let relation_attrs: Vec<usize> = util::parse_comma_list(ra_str)?;
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let known_keys: Vec<Vec<usize>> = match args.known_keys.as_deref() {
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Some(s) if !s.is_empty() => s
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.split(';')
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.map(|k| util::parse_comma_list(k.trim()))
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.collect::<Result<Vec<_>>>()?,
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_ => vec![],
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};
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(
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ser(AdditionalKey::new(
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num_attributes,
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dependencies,
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relation_attrs,
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known_keys,
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))?,
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resolved_variant.clone(),
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)
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}
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// SubsetSum
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"SubsetSum" => {
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let sizes_str = args.sizes.as_deref().ok_or_else(|| {
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domain_size: None,
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relations: None,
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conjuncts_spec: None,
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relation_attrs: None,
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known_keys: None,
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costs: None,
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cut_bound: None,
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size_bound: None,

‎src/lib.rs‎

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@@ -60,13 +60,14 @@ pub mod prelude {
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UndirectedTwoCommodityIntegralFlow,
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};
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pub use crate::models::misc::{
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BinPacking, BoyceCoddNormalFormViolation, CbqRelation, ConjunctiveBooleanQuery,
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ConjunctiveQueryFoldability, Factoring, FlowShopScheduling, Knapsack,
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LongestCommonSubsequence, MinimumTardinessSequencing, MultiprocessorScheduling, PaintShop,
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Partition, QueryArg, RectilinearPictureCompression, ResourceConstrainedScheduling,
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SequencingToMinimizeMaximumCumulativeCost, SequencingWithReleaseTimesAndDeadlines,
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SequencingWithinIntervals, ShortestCommonSupersequence, StaffScheduling,
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StringToStringCorrection, SubsetSum, SumOfSquaresPartition, Term,
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AdditionalKey, BinPacking, BoyceCoddNormalFormViolation, CbqRelation,
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ConjunctiveBooleanQuery, ConjunctiveQueryFoldability, Factoring, FlowShopScheduling,
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Knapsack, LongestCommonSubsequence, MinimumTardinessSequencing, MultiprocessorScheduling,
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PaintShop, Partition, QueryArg, RectilinearPictureCompression,
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ResourceConstrainedScheduling, SequencingToMinimizeMaximumCumulativeCost,
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SequencingWithReleaseTimesAndDeadlines, SequencingWithinIntervals,
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ShortestCommonSupersequence, StaffScheduling, StringToStringCorrection, SubsetSum,
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SumOfSquaresPartition, Term,
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};
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pub use crate::models::set::{
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ComparativeContainment, ConsecutiveSets, ExactCoverBy3Sets, MaximumSetPacking,

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