Competitive Landscape

Why Navokoj Wins#

Market Comparison#

Capability	Navokoj	Gurobi/CPLEX	OR-Tools	Classical CDCL
Variables	Up to 1M+	100M+	1M+	1M
Millisecond solve	✅	❌	❌	❌
Hardness prediction	✅ DEFEKT	❌	❌	❌
Always returns result	✅ Anytime	❌ Timeout	❌ Timeout	❌ UNSAT
XOR-native	✅	❌	❌	❌
GPU-accelerated	✅ H100	Partial	❌	❌
Developer API	✅ REST	❌ SDK	✅	✅
Pay-per-use	✅	❌ License	❌ License	❌

Gurobi vs Navokoj#

Gurobi is the industry standard for mathematical optimization. It’s excellent for:

Linear/quadratic programming
MILP (mixed integer linear programming)
Continuous variable optimization

Navokoj excels where Gurobi struggles:

Boolean satisfiability at scale
Problems with complex logical constraints
Real-time decisioning (< 1 second)
Problems where hardness is unknown

Scenario	Gurobi	Navokoj
10k variable routing	10-60s	< 1s
Million-variable placement	May timeout	347ms
Complex boolean logic	Requires translation	Native
Unknown hardness	No visibility	DEFEKT
UNSAT instance	Fails	Best effort

OR-Tools vs Navokoj#

OR-Tools (Google) is open-source and widely used for:

Vehicle routing
Scheduling
Integer programming

Navokoj provides advantages:

Native boolean SAT
Much higher satisfaction rates
Physics-inspired optimization
DEFEKT pre-solve diagnostics

Scenario	OR-Tools	Navokoj
5k vehicle routing	30s-5min	< 1s
Complex boolean logic	Requires CP-SAT	Native
Satisfaction guarantee	Best effort	92.57% industrial
Hardness visibility	None	DEFEKT

Classical CDCL SAT Solvers#

Kissat, CaDiCaL, Maplesat are competition-grade CDCL solvers. They excel at proving UNSAT and finding exact solutions on structured problems.

Navokoj differs fundamentally:

CDCL = Systematic search through boolean assignment space
Navokoj = Continuous optimization on arithmetic manifold

Capability	CDCL Solvers	Navokoj
Structured industrial (multipliers, timetabling)	Strong	Strong
Expander / random hard	Strong	~90% plateau
XOR constraints	Gaussian elimination	Continuous
Real-time (< 100ms)	❌	✅
Always returns result	❌ UNSAT/timeout	Anytime
Million-variable scale	On structured problems	On structured problems
GPU acceleration	Rare	H100

CDCL solvers are exact solvers — when they find a solution or prove UNSAT, the answer is certified. Navokoj is an anytime approximator — it always returns a result, but doesn’t produce unsatisfiability proofs. Choose based on your requirement: certify correctness (CDCL) or get the best available result fast (Navokoj).

Our Differentiation#

1. Real-Time Anytime#

Classical solvers: UNSAT → Done, no partial result. Navokoj: Always returns the best available assignment.

2. Structured Industrial Scale#

On problems with regular structure (hardware multipliers, timetabling, grid problems), Navokoj achieves:

Problem	Scale	Satisfaction	Time
Hardware multiplier	788K vars, 2.6M clauses	100%	5.92s
Enterprise timetabling	147K vars, 80M clauses	100%	73s
Grid coloring	4M vars, 15M clauses	100%	475s

CDCL solvers are strong on structured problems too — these aren’t cherry-picked comparisons. The difference is that Navokoj delivers high satisfaction consistently within a time bound, while CDCL may timeout or require exponential time on unfavorable instances.

3. Hardness Visibility#

Before you solve, DEFEKT tells you:

{
  "solvability_score": 84,
  "status": "likely_solvable",
  "recommendation": "Use pro-deepthink on H100 GPU"
}

No other solver offers this.

4. Anytime Algorithm Guarantee#

Classical solvers: UNSAT → Done, no result.

Navokoj: Always returns the best partial assignment.

{
  "success": true,
  "satisfiable": false,
  "satisfaction_rate": 0.985,
  "timeout_budget_hit": true,
  "assignment": [true, false, ...]
}

When to Use What#

Use Case	Recommended
Linear programming	Gurobi
MILP with continuous vars	Gurobi/CPLEX
Vehicle routing (simple)	OR-Tools
Boolean SAT at scale	Navokoj
Real-time decisioning	Navokoj
Complex logical constraints	Navokoj
Unknown problem hardness	Navokoj
Must have partial result	Navokoj

The Bottom Line#

Requirement	Solution
Speed matters	Navokoj
Scale matters	Navokoj
Hardness unknown	Navokoj
Can’t afford empty results	Navokoj
Complex boolean logic	Navokoj
MILP with continuous vars	Gurobi
Linear programming	Gurobi
Simple VRP	OR-Tools

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