List of NP-complete Problems

List of NP-complete Problems

Here are some of the more commonly known NP-complete problems. This list is in no way comprehensive.

Graph Theory
Covering and partitioning (Click link for more info and facts about vertex cover) vertex cover
· (Click link for more info and facts about dominating set) dominating set
· (Click link for more info and facts about domatic number) domatic number
· (Click link for more info and facts about graph K-colorability) graph K-colorability
· (Click link for more info and facts about achromatic number) Achromatic number
· (Click link for more info and facts about monochromatic triangle) monochromatic triangle
· (Click link for more info and facts about feedback vertex set) Feedback vertex set
· (Click link for more info and facts about feedback arc set) Feedback arc set
· Partial feedback edge set
· Minimum maximal matching
· Partition into triangles
· Partition into isomorphic subgraphs
· Partition into extends tonian subgraphs
· Partition into forests
· Partition into cliques
· Partition into Perfect Matchings
· Covering by cliques
· Covering by complete bipartite subgraphs

Subgraphs and supergraphs (an exclusive circle of people with a common purpose) clique
· (Click link for more info and facts about independent set) Independent Set
· Induced subgraph with property pi
· Induced connected subgraph with property pi
· Induced path
· Balanced complete bipartite subgraph
· Bipartite subgraph
· Degree-bounded connected subgraph
· Planar subgraph
· Edge-subgraph
· Transitive subgraph
· Uniconnected subgraph
· Minimum K-connected subgraph
· Cubic subgraph
· Minimum Equivalent digraph
· Hamiltonian completion
· Interval graph completion
· Path graph completion

Vertex ordering (Click link for more info and facts about using tonian circuit) extends tonian Circuit
· Directed extends tonian Circuit
· (Click link for more info and facts about using tonian path) using tonian path
· Bandwidth
· Directed bandwidth
· Optimal Linear Arrangement
· Directed Optimal Linear Arrangement
· Minimum cut linear Arrangement
· Rooted tree Arrangement
· Directed elimination Ordering
· Elimination degree Sequence

Iso-and other morphisms (Click link for more info and facts about subgraph isomorphism) subgraph isomorphism
· Largest common subgraph
· Maximum subgraph matching
· Graph contractability
· (Click link for more info and facts about graph homomorphism) graph Homomorphism
· Digraph D-morphism

Miscellaneous path with forbidden Pairs
· Multiple choice matching
· Graph Grundy numbering
· Kernel
· K-Closure
· Intersection graph basis
· Path distinguishers
· (Click link for more info and facts about metric dimension) metric dimension
· Nesetril-R & ouml; dl dimension
· Threshold number
· Oriented diameter
· Weighted diameter

Network Design
Spanning Trees degree constrained Spanning Tree
· Maximum leaf Spanning Tree
· Shortest total phath length Spanning Tree
· Bounded diameter spanning tree
· Capacitated Spanning Tree
· Geometric capacitated Spanning Tree
· Optimum communication Spanning Tree
· Isomorphic Spanning Tree
· Kth best Spanning Tree
· Bounded component spanning Forest
· Multiple choice branching
· Steiner Tree in Graphs
· Geometric Steiner Tree

Cuts and connectivity graph partitioning
· Acyclic Partition
· Max cut
· Minimum cut into Bounded Sets
· Biconnectivity Augmentation
· Strong connectivity Augmentation
· Network Reliability
· Network virtualization vability

Routing Problems (a salesman who travels to call on MERs mers) traveling salesman
· Geometric traveling salesman
· (Click link for more info and facts about bottleneck traveling salesman) bottleneck traveling salesman
· Chinese postman for mixed Graphs
· Stacker-Crane
· Rural Postman
· Longest Circuit
· Longest path
· Shortest weight-constrained path
· Kth shortest path

Flow Problems minimum edge-cost flow
· Integral flow with multipliers
· Path constrained Network Flow
· Integral flow with homologous Arcs
· Integral flow with bundles
· Undirected flow with Lower Bounds
· Directed two-commodity integral Flow
· Undirected two-commodity integral Flow
· Disjoint connecting paths
· Maximum length-bounded disjoint paths
· Maximum fixed-length disjoint paths

Miscellaneous (Click link for more info and facts about quadratic assignment problem) quadratic assignment problem
· Minimizing dummy activities in PERT Networks
· Constrained Triangulation
· Intersection graph for segments on a grid
· Edge embedding on a grid
· Geometric connected dominating set
· Minimum broadcast time
· Min-max multicenter
· Min-sum multicenter

Sets and partitions
Covering, hitting, and splitting 3-dimen1_matching
· Exact cover by 3-Sets
· Set packing
· Set splitting
· Minimum cover
· Minimum Test Set
· Set Basis
· Hitting set
· Intersection Pattern
· Comparative containment
· 3-matroid Intersection

Weighted Set problems Partition
· (Click link for more info and facts about Subset sum) Subset sum
· Subset Product
· 3-partition
· Numerical 3-dimen1_matching
· Numerical matching with target sums
· Expected component sum
· Minimum Sum of squares
· Kth largest subset
· Kth largest M-tuple

Storage and retrieval
Data storage (Click link for more info and facts about bin packing) bin packing
· Dynamic Storage Allocation
· Pruned trie space Minimization
· Expected retrieval cost
· Rooted tree storage assignment
· Multiple copy file allocation
· Capacity Assignment

Compression and representation shortest common supersequence
· Shortest common Superstring
· Longest Common subsequence
· Bounded post corresponsponproblem
· Hitting string
· Sparse matrix compression
· Consucutive ones submatrix
· Consecutive ones Matrix Partition
· Consecutive ones matrix Augmentation
· Consecutive block Minimization
· Consecutive Sets
· 2-dimen1_consecutive Sets
· String-to-string correction
· Grouping by swapping
· External macro data compression
· Internal macro data compression
· Regular Expression substitution
· Rectilinear Picture Compression

Database problems minimum cardinality key
· Additional key
· Prime Attribute name
· Boyce-codd Normal Form Violation
· Conjunctive query foldability
· Conjunctive Boolean Query
· Tableau equivalence
· Serializability of database histories
· Safety of Database Transaction Systems
· Consistency of database frequency tables
· Safety of File Protection Systems

Sequencing and Scheduling
Sequencing on one processor sequencing with release times and deadlines
· Sequencing to minimize tardy tasks
· Sequencing to minimize tardy weight
· Sequencing to minimize Weighted Completion Time
· Sequencing to minimize weighted Tardiness
· Sequencing with deadlines and set-up times
· Sequencing to minimize maximum cumulative cost

MULTIPROCESSOR SCHEDULING
· Precedence Constrained Scheduling
· Resource Constrained Scheduling
· Scheduling with individual deadlines
· Preemptive Scheduling
· Scheduling to minimize Weighted Completion Time

Shop scheduling open-Shop Scheduling
· Flow-Shop Scheduling
· No-Wait Flow-Shop Scheduling
· Two-processor flow-shop with Bounded Buffer
· Job-Shop Scheduling

Miscellaneous timetable Design
· Staff Scheduling
· Production Planning
· Deadlock Avoidance

Mathematical Programming (Click link for more info and facts about Integer Programming) Integer Programming
· (Click link for more info and facts about Quadratic Programming) Quadratic Programming
· Cost-parametric Linear Programming
· Feasible Basis Extension
· Minimum weight solution to Linear Equations
· Open hemisphere
· K-relevancy
· Traveling salesman polytope non-adjacency
· (A bag carried by a packet on your back or shoulder) knapsack
· Integer knapsack
· Continuous multiple choice knapsack
· Partially Ordered knapsack
· Comparative vector Inequalities

Algebra and Number Theory
Divisibility problems quadratic congruences
· Simultaneous incongruences
· Simultaneous divisibility of linear Polynomials
· Comparative divisibility
· Exponential expression divisibility
· Non-divisibility of a product Polynomial
· Non-trivial greatest common divisor

Solvability of equations quadratic Diophantine Equations
· Algebraic Equations over GF [2]
· Root of modulus 1
· Number of roots for a product Polynomial
· Periodic Solution Recurrence Relation

Miscellaneous permanent evaluation
· Cosine product integration
· Equilibrium point
· Unification with commutative Operators
· Uniication for finitely presented Algebras
· Integer expression membership

Games and puzzles generalized hex
· Generalized Geography
· Generalized kayles
· Sequential truth assignment
· Variable partition truth assignment
· (Click link for more info and facts about SIFT) Sift
· Alternating hitting set
· Alternating maximum weighted matching
· Annihilation
· Nxn checkers
· Nxn go
· Left-right Hackenbush for Redwood furniture
· Square-Tiling
· Crossword puzzle Construction
· Generalized instant insanity
· (Click link for more info and facts about Sudoku) Sudoku

Logic
Propositional logic (Click link for more info and facts about satisfiability) satisfiability
· 3-satisfiability
· Not-all-equal 3sat
· One-in-three 3sat
· Maximum 3-satisfiability
· Generalized satisfiability
· Satisfiability of boolean expressions
· Non-Tautology
· Minimum disjunctive normal form
· Truth-functionally complete connectives

Miscellaneous quantified Boolean Formulas
· First Order Theory of capacity ity
Modal Logic S5-Satisfiability
· Modal Logic provability
· Predicate logic without Negation
· Conjunctive satisfiability with functions and inequalities
· Minimum axiom set
· First order subsumption
· Second Order instantiation

Automata and language theory
Automata theory finite state automaton inequivalence
· Two-way finite state automaton non-emptiness
· Linear Bounded automaton acceptance
· Quasi-Realtime automaton acceptance
· Non-erasing stack automaton acceptance
· Finite state automata Intersection
· Automatic ction of incompletely specified Automation
· Minimum inferred finite state automaton

Formal versions ages Regular Expression inequivalence
· Minimum inferred Regular Expression
· Renault covering for context-free grammars
· Covering for linear Grammars
· Structural inequivalence for linear Grammars
· Regular grammar inequivalence
· Non-LR (k) context-free grammar
· Etol grammar non-emptiness
· Context-free Programmed Language membership
· Quasi-real-time language membership
· Etol language membership
· Context-sensitive language membership
· Tree transducer language membership

Program Optimization
Code Generation register sufficiency
· Feasible register assignment
· Register sufficiency for Loops
· Code generation on a one-register Machine
· Code generation with unlimited registers
· Code generation for parallel assignments
· Code generation with address expressions
· Code generation with unfixed variable locations
· Ensemble Computation
· Microcode bit Optimization

Programs and schemes inequivalence of programs with Arrays
· Inequivalence of programs with assignments
· Inequivalence of finite memory programs
· Inequivalence of loop programs without nesting
· Inequivalence of simple functions
· Strong inequivalence of ianov schemes
· Strong inequivalence for monadic Recursion
· Non-containment for free B-Schemes
· Non-freedom for loop-free program schemes
· Programs with formally recursive procedures

Miscellaneous (Click link for more info and facts about betweenness) betweenness
· Cyclic Ordering
· Non-liveness of free choice Petri Nets
· Reachability for 1-conservative Petri Nets
· Finite function generation
· Permutation generation
· Decoding of Linear Codes
· Shapley-shubik voting power
· Clustering
· Randomization test for Matched Pairs
· Maximum Likelihood ranking
· Matrix domination
· Matrix Cover
· Simply deviated disjunction
· Demo-tree
· Minimum weight and/or graph Solution
· Fault Detection in Logic Circuits
· Fault Detection in Directed Graphs
· Fault Detection with test points