Remove QuadraticProgramming model (#528) — mislabeled bounded-integer variant under MP2 name

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

Author: isPANN

docs/paper/reductions.typ

@@ -317,7 +317,6 @@
   "PreemptiveScheduling": [Preemptive Scheduling],
   "PrimeAttributeName": [Prime Attribute Name],
   "QuadraticAssignment": [Quadratic Assignment],
-  "QuadraticProgramming": [Quadratic Programming],
   "EquilibriumPoint": [Equilibrium Point],
   "QuadraticCongruences": [Quadratic Congruences],
   "QuadraticDiophantineEquations": [Quadratic Diophantine Equations],
@@ -5221,34 +5220,6 @@ In all graph problems below, $G = (V, E)$ denotes an undirected graph with $|V|
   ]
 }
 
-#{
-  let x = load-model-example("QuadraticProgramming")
-  let m = x.instance.num_vars
-  let K = x.instance.bound
-  let c = x.instance.quad_coeffs
-  let d = x.instance.lin_coeffs
-  let sol = (config: x.optimal_config, metric: x.optimal_value)
-  let fstar = metric-value(sol.metric)
-  let ystar = sol.config.map(ci => ci - K)
-  let ystar-disp = ystar.map(v => str(v)).join(", ")
-  [
-    #problem-def("QuadraticProgramming")[
-      Given a positive integer $m$, a positive integer bound $K >= 1$, a finite set $X$ of pairs $(bold(x), b)$ where $bold(x) in ZZ^m$ and $b in RR$, and two $m$-tuples $bold(c), bold(d) in RR^m$, find $bold(y) in {-K, -K+1, dots, K}^m$ that minimises
-      $ sum_(i=1)^m (c_i y_i^2 + d_i y_i) quad "subject to" quad bold(x) dot bold(y) <= b "for every" (bold(x), b) in X. $
-    ][
-      Bounded Integer Quadratic Programming is the discrete restriction of Garey & Johnson's QUADRATIC PROGRAMMING (MP2) @garey1979 in which each component of the decision vector is forced to lie in the finite integer box ${-K, dots, K}$. The fully continuous (rational) case is also NP-complete: it was open in @garey1979 and resolved by Vavasis @vavasis1990, who proved that QP belongs to NP. NP-hardness of the bounded integer variant follows from Sahni's @sahni1974 PARTITION $arrow$ QP reduction, whose constructed instance has its optimum on ${0,1}^m subset.eq {-K, dots, K}^m$ for every $K >= 1$. Bounded Integer QP strictly generalises QUBO (the case $K = 1$ collapses to QUBO with linear side constraints after the affine substitution $z_i = (y_i + 1)/2$), so it inherits a brute-force bound of $O^*((2K+1)^m)$#footnote[No algorithm improving on enumeration over the discrete box ${-K, dots, K}^m$ is known for general non-convex bounded integer QP.].
-
-      *Example.* Consider the PARTITION instance $bold(a) = (1, 1, 2)$ with total sum $4$ and target $S/2 = 2$. Sahni's encoding sets $bold(c) = (#c.map(v => str(int(v))).join(", "))$, $bold(d) = (#d.map(v => str(int(v))).join(", "))$, and adds five linear constraints to restrict each $y_i$ to ${0, 1}$ and to force $bold(a) dot bold(y) = 2$:
-      $ y_1, y_2, y_3 >= 0, quad y_1 + y_2 + 2 y_3 <= 2, quad y_1 + y_2 + 2 y_3 >= 2. $
-      Over the $#(calc.pow(2 * K + 1, m))$ configurations in ${-1, 0, 1}^3$ exactly two are feasible: $bold(y) = (1, 1, 0)$ with objective $0$ and $bold(y) = (0, 0, 1)$ with objective $1$. The optimum is $bold(y)^* = (#ystar-disp)$ with $sum_i (c_i y_i^2 + d_i y_i) = #fstar$, recovering the PARTITION witness ${a_1, a_2}$.
-
-      #pred-commands(
-        "pred solve quadratic-programming.json --solver brute-force",
-      )
-    ]
-  ]
-}
-
 #{
   let x = load-model-example("AlgebraicEquationsOverGF2")
   let n = x.instance.num_variables

docs/paper/references.bib

@@ -452,17 +452,6 @@ @article{sahni1974
   year    = {1974}
 }
 
-@article{vavasis1990,
-  author  = {Stephen A. Vavasis},
-  title   = {Quadratic programming is in {NP}},
-  journal = {Information Processing Letters},
-  volume  = {36},
-  number  = {2},
-  pages   = {73--77},
-  year    = {1990},
-  doi     = {10.1016/0020-0190(90)90100-C}
-}
-
 @article{abdelWahabKameda1978,
   author  = {H. M. Abdel-Wahab and T. Kameda},
   title   = {Scheduling to Minimize Maximum Cumulative Cost Subject to Series-Parallel Precedence Constraints},

problemreductions-cli/src/commands/create.rs

@@ -620,10 +620,10 @@ pub fn create(args: &CreateArgs, out: &OutputConfig) -> Result<()> {
         return create_random(args, canonical, &resolved_variant, out);
     }
 
-    // ILP, CircuitSAT, and QuadraticProgramming have complex input structures
+    // ILP and CircuitSAT have complex input structures
     // not suited for CLI flags. Check before the empty-flags help so they get a
     // clear message.
-    if canonical == "ILP" || canonical == "CircuitSAT" || canonical == "QuadraticProgramming" {
+    if canonical == "ILP" || canonical == "CircuitSAT" {
         bail!(
             "CLI creation is not yet supported for {canonical}.\n\n\
              {canonical} instances are typically created via reduction:\n\

src/lib.rs

@@ -45,7 +45,7 @@ pub mod prelude {
     pub use crate::models::algebraic::{
         AlgebraicEquationsOverGF2, ConsecutiveOnesMatrixAugmentation,
         MinimumWeightSolutionToLinearEquations, QuadraticAssignment, QuadraticCongruences,
-        QuadraticProgramming, SimultaneousIncongruences, SparseMatrixCompression, BMF, QUBO,
+        SimultaneousIncongruences, SparseMatrixCompression, BMF, QUBO,
     };
     pub use crate::models::formula::{
         CNFClause, CircuitSAT, KSatisfiability, Maximum2Satisfiability, NAESatisfiability,

src/models/algebraic/mod.rs

@@ -12,7 +12,6 @@
 //! - [`QuadraticAssignment`]: Quadratic Assignment Problem
 //! - [`QuadraticCongruences`]: Decide x² ≡ a (mod b) for x in {1, ..., c-1}
 //! - [`QuadraticDiophantineEquations`]: Decide ax² + by = c in positive integers
-//! - [`QuadraticProgramming`]: Bounded Integer Quadratic Programming
 //! - [`SimultaneousIncongruences`]: Decide whether x ≢ aᵢ (mod bᵢ) for all i simultaneously
 //! - [`MinimumMatrixDomination`]: Minimum Matrix Domination (minimum dominating set of 1-entries)
 //! - [`MinimumWeightDecoding`]: Minimum Weight Decoding (minimize Hamming weight of Hx≡s mod 2)
@@ -35,7 +34,6 @@ pub(crate) mod minimum_weight_solution_to_linear_equations;
 pub(crate) mod quadratic_assignment;
 pub(crate) mod quadratic_congruences;
 pub(crate) mod quadratic_diophantine_equations;
-pub(crate) mod quadratic_programming;
 pub(crate) mod qubo;
 pub(crate) mod simultaneous_incongruences;
 pub(crate) mod sparse_matrix_compression;
@@ -56,7 +54,6 @@ pub use minimum_weight_solution_to_linear_equations::MinimumWeightSolutionToLine
 pub use quadratic_assignment::QuadraticAssignment;
 pub use quadratic_congruences::QuadraticCongruences;
 pub use quadratic_diophantine_equations::QuadraticDiophantineEquations;
-pub use quadratic_programming::QuadraticProgramming;
 pub use qubo::QUBO;
 pub use simultaneous_incongruences::SimultaneousIncongruences;
 pub use sparse_matrix_compression::SparseMatrixCompression;
@@ -80,7 +77,6 @@ pub(crate) fn canonical_model_example_specs() -> Vec<crate::example_db::specs::M
     specs.extend(quadratic_assignment::canonical_model_example_specs());
     specs.extend(quadratic_congruences::canonical_model_example_specs());
     specs.extend(quadratic_diophantine_equations::canonical_model_example_specs());
-    specs.extend(quadratic_programming::canonical_model_example_specs());
     specs.extend(equilibrium_point::canonical_model_example_specs());
     specs.extend(simultaneous_incongruences::canonical_model_example_specs());
     specs.extend(sparse_matrix_compression::canonical_model_example_specs());

src/models/algebraic/quadratic_programming.rs

@@ -15,7 +15,7 @@ pub use algebraic::{
     ConsecutiveOnesMatrixAugmentation, ConsecutiveOnesSubmatrix, EquilibriumPoint,
     FeasibleBasisExtension, MinimumMatrixCover, MinimumMatrixDomination, MinimumWeightDecoding,
     MinimumWeightSolutionToLinearEquations, QuadraticAssignment, QuadraticCongruences,
-    QuadraticDiophantineEquations, QuadraticProgramming, SimultaneousIncongruences,
+    QuadraticDiophantineEquations, SimultaneousIncongruences,
     SparseMatrixCompression, BMF, ILP, QUBO,
 };
 pub use decision::Decision;