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标题: List of NP-complete problems  
 
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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 Hamiltonian 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 Hamiltonian circuit) Hamiltonian circuit
· Directed Hamiltonian circuit
·  (Click link for more info and facts about Hamiltonian path) Hamiltonian 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-Rödl 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 survivability

Routing problems  (A salesman who travels to call on customers) 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-dimensional 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-dimensional 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 correspondence problem
· Hitting string
· Sparse matrix compression
· Consucutive ones submatrix
· Consecutive ones matrix partition
· Consecutive ones matrix augmentation
· Consecutive block minimization
· Consecutive sets
· 2-dimensional 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 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 strap 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
· Unification 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 equality
· 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
· Reduction of incompletely specified automata
· Minimum inferred finite state automaton

Formal languages Regular expression inequivalence
· Minimum inferred regular expression
· Reynolds 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
· Decision tree
· Minimum weight and/or graph solution
· Fault detection in logic circuits
· Fault detection in directed graphs
· Fault detection with test points




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2006-4-24 15:31#1
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