The Complete List
The Complete List
the complete list, the complete listening and speaking course, the complete listening-speaking, the complete listening and speaking course david christiansen.
 
 
 
 
 
 
Go Back

Smartphone









Free the Animation VR / AR
Play to reveal 3D images and 3D models!
Demonstration A-Frame / Multiplayer
Android app on Google Play
 
vlrPhone / vlrFilter
Project of very low consumption, radiation and bitrate softphones, with the support of the spatial audio, of the frequency shifts and of the ultrasonic communications / Multifunction Audio Filter with Remote Control!



 

Vectors and 3D Models

City Images, Travel Images, Safe Images

Howto - How To - Illustrated Answers

 

List of NP-complete problems
This is a list of some of the more commonly known problems that are NP-complete when expressed as decision problems. As there are hundreds of such problems

View Wikipedia Article

This is a dynamic list and may never be able to satisfy particular standards for completeness. You can help by expanding it with reliably sourced entries.

This is a list of some of the more commonly known problems that are NP-complete when expressed as decision problems. As there are hundreds of such problems known, this list is in no way comprehensive. Many problems of this type can be found in Garey & Johnson (1979).

Contents
  • 1 Graphs and hypergraphs
  • 2 Mathematical programming
  • 3 Formal languages and string processing
  • 4 Games and puzzles
  • 5 Other
  • 6 See also
  • 7 Notes
  • 8 References
  • 9 External links
Graphs and hypergraphs

Graphs occur frequently in everyday applications. Examples include biological or social networks, which contain hundreds, thousands and even billions of nodes in some cases (e.g. Facebook or LinkedIn).

  • 1-planarity[1]
  • 3-dimensional matching[2][3]
  • Bipartite dimension[4]
  • Capacitated minimum spanning tree[5]
  • Route inspection problem (also called Chinese postman problem) for mixed graphs (having both directed and undirected edges). The program is solvable in polynomial time if the graph has all undirected or all directed edges. Variants include the rural postman problem.[6]
  • Clique problem[2][7]
  • Complete coloring, a.k.a. achromatic number[8]
  • Domatic number[9]
  • Dominating set, a.k.a. domination number[10]
NP-complete special cases include the edge dominating set problem, i.e., the dominating set problem in line graphs. NP-complete variants include the connected dominating set problem and the maximum leaf spanning tree problem.[11]
  • Bandwidth problem[12]
  • Clique cover problem[2][13]
  • Rank coloring a.k.a. cycle rank
  • Degree-constrained spanning tree[14]
  • Exact cover problem. Remains NP-complete for 3-sets. Solvable in polynomial time for 2-sets (this is a matching).[2][15]
  • Feedback vertex set[2][16]
  • Feedback arc set[2][17]
  • Graph homomorphism problem[18]
  • Graph coloring[2][19]
  • Graph partition into subgraphs of specific types (triangles, isomorphic subgraphs, Hamiltonian subgraphs, forests, perfect matchings) are known NP-complete. Partition into cliques is the same problem as coloring the complement of the given graph. A related problem is to find a partition that is optimal terms of the number of edges between parts.[20]
  • Hamiltonian completion[21]
  • Hamiltonian path problem, directed and undirected.[2][22]
  • Longest path problem[23]
  • Maximum bipartite subgraph or (especially with weighted edges) maximum cut.[2][24]
  • Maximum independent set[25]
  • Maximum Induced path[26]
  • Graph intersection number[27]
  • Metric dimension of a graph[28]
  • Minimum k-cut
  • Steiner tree, or Minimum spanning tree for a subset of the vertices of a graph.[2] (The minimum spanning tree for an entire graph is solvable in polynomial time.)
  • Modularity maximization[29]
  • Pathwidth[30]
  • Set cover (also called minimum cover problem) This is equivalent, by transposing the incidence matrix, to the hitting set problem.[2][31]
  • Set splitting problem[32]
  • Shortest total path length spanning tree[33]
  • Slope number two testing[34]
  • Treewidth[30]
  • Vertex cover[2][35]
Mathematical programming
  • 3-partition problem[36]
  • Bin packing problem[37]
  • Knapsack problem, quadratic knapsack problem, and several variants[2][38]
  • Variations on the Traveling salesman problem. The problem for graphs is NP-complete if the edge lengths are assumed integers. The problem for points on the plane is NP-complete with the discretized Euclidean metric and rectilinear metric. The problem is known to be NP-hard with the (non-discretized) Euclidean metric.[39]
  • Bottleneck traveling salesman[40]
  • Integer programming. The variant where variables are required to be 0 or 1, called zero-one linear programming, and several other variants are also NP-complete[2][41]
  • Latin squares (The problem of determining if a partially filled square can be completed to form one)
  • Numerical 3-dimensional matching[42]
  • Partition problem[2][43]
  • Quadratic assignment problem[44]
  • Quadratic programming (NP-hard in some cases, P if convex)
  • Subset sum problem[45]
Formal languages and string processing
  • Closest string[46]
  • Longest common subsequence problem[47]
  • The bounded variant of the Post correspondence problem[48]
  • Shortest common supersequence[49]
  • String-to-string correction problem[50]
Games and puzzles
  • Battleship
  • Bulls and Cows, marketed as Master Mind: certain optimisation problems but not the game itself.
  • Eternity II
  • (Generalized) FreeCell[51]
  • Fillomino[52]
  • Hashiwokakero[53]
  • Heyawake[54]
  • (Generalized) Instant Insanity[55]
  • Kakuro (Cross Sums)
  • Kuromasu (also known as Kurodoko)[56]
  • Lemmings (with a polynomial time limit)[57]
  • Light Up[58]
  • Masyu[59]
  • Minesweeper Consistency Problem[60] (but see Scott, Stege, & van Rooij[61])
  • Nimber (or Grundy number) of a directed graph.[62]
  • Numberlink
  • Nonograms
  • Nurikabe
  • Rubik's Cube (solved optimally)
  • SameGame
  • Slither Link on a variety of grids[63][64][65]
  • (Generalized) Sudoku[63][66]
  • Problems related to Tetris[67]
  • Verbal arithmetic
Other
  • Art gallery problem and its variations.
  • Berth allocation problem[68]
  • Betweenness
  • Assembling an optimal Bitcoin block.[69]
  • Boolean satisfiability problem (SAT).[2][70] There are many variations that are also NP-complete. An important variant is where each clause has exactly three literals (3SAT), since it is used in the proof of many other NP-completeness results.[71]
  • Conjunctive Boolean query[72]
  • Cyclic ordering
  • Circuit satisfiability problem
  • Uncapacitated Facility Location
  • Flow Shop Scheduling Problem
  • Generalized assignment problem
  • Upward planarity testing[34]
  • Hospitals-and-residents problem with couples
  • Some problems related to Job-shop scheduling
  • Monochromatic triangle[73]
  • Minimum maximal independent set a.k.a. minimum independent dominating set[74]
NP-complete special cases include the minimum maximal matching problem,[75] which is essentially equal to the edge dominating set problem (see above).
  • Maximum common subgraph isomorphism problem[76]
  • Minimum degree spanning tree
  • Minimum k-spanning tree
  • Metric k-center
  • Maximum 2-Satisfiability[77]
  • Modal logic S5-Satisfiability
  • Some problems related to Multiprocessor scheduling
  • Maximum volume submatrix – Problem of selecting the best conditioned subset of a larger m x n matrix. This class of problem is associated with Rank revealing QR factorizations and D optimal experimental design.[78]
  • Minimal addition chains for sequences.[79] The complexity of minimal addition chains for individual numbers is unknown.[80]
  • Non-linear univariate polynomials over GF, n the length of the input. Indeed, over any GF.
  • Open-shop scheduling
  • Pathwidth,[30] or, equivalently, interval thickness, and vertex separation number[81]
  • Pancake sorting distance problem for strings[82]
  • k-Chinese postman
  • Subgraph isomorphism problem[83]
  • Variations of the Steiner tree problem. Specifically, with the discretized Euclidean metric, rectilinear metric. The problem is known to be NP-hard with the (non-discretized) Euclidean metric.[84]
  • Set packing[2][85]
  • Serializability of database histories[86]
  • Scheduling to minimize weighted completion time
  • Sparse approximation
  • Block Sorting[87] (Sorting by Block Moves)
  • Second order instantiation
  • Treewidth[30]
  • Testing whether a tree may be represented as Euclidean minimum spanning tree
  • Three-dimensional Ising model[88]
  • Vehicle routing problem
See also
  • Existential theory of the reals#Complete problems
  • Karp's 21 NP-complete problems
  • List of PSPACE-complete problems
  • Reduction (complexity)
Notes
  1. ^ Grigoriev & Bodlaender (2007).
  2. ^ a b c d e f g h i j k l m n o p q Karp (1972)
  3. ^ Garey & Johnson (1979): SP1
  4. ^ Garey & Johnson (1979): GT18
  5. ^ Garey & Johnson (1979): ND5
  6. ^ Garey & Johnson (1979): ND25, ND27
  7. ^ Garey & Johnson (1979): GT19
  8. ^ Garey & Johnson (1979): GT5
  9. ^ Garey & Johnson (1979): GT3
  10. ^ Garey & Johnson (1979): GT2
  11. ^ Garey & Johnson (1979): ND2
  12. ^ Garey & Johnson (1979): GT40
  13. ^ Garey & Johnson (1979): GT17
  14. ^ Garey & Johnson (1979): ND1
  15. ^ Garey & Johnson (1979): SP2
  16. ^ Garey & Johnson (1979): GT7
  17. ^ Garey & Johnson (1979): GT8
  18. ^ Garey & Johnson (1979): GT52
  19. ^ Garey & Johnson (1979): GT4
  20. ^ Garey & Johnson (1979): GT11, GT12, GT13, GT14, GT15, GT16, ND14
  21. ^ Garey & Johnson (1979): GT34
  22. ^ Garey & Johnson (1979): GT37, GT38, GT39
  23. ^ Garey & Johnson (1979): ND29
  24. ^ Garey & Johnson (1979): GT25, ND16
  25. ^ Garey & Johnson (1979): GT20
  26. ^ Garey & Johnson (1979): GT23
  27. ^ Garey & Johnson (1979): GT59
  28. ^ Garey & Johnson (1979): GT61
  29. ^ Brandes, Ulrik; Delling, Daniel; Gaertler, Marco; Görke, Robert; Hoefer, Martin; Nikoloski, Zoran; Wagner, Dorothea (2006), Maximizing Modularity is hard, arXiv:physics/0608255 , Bibcode:2006physics...8255B 
  30. ^ a b c d Arnborg, Corneil & Proskurowski (1987)
  31. ^ Garey & Johnson (1979): SP5, SP8
  32. ^ Garey & Johnson (1979): SP4
  33. ^ Garey & Johnson (1979): ND3
  34. ^ a b "On the computational complexity of upward and rectilinear planarity testing". Lecture Notes in Computer Science. 894/1995. 1995. pp. 286–297. doi:10.1007/3-540-58950-3_384. 
  35. ^ Garey & Johnson (1979): GT1
  36. ^ Garey & Johnson (1979): SP15
  37. ^ Garey & Johnson (1979): SR1
  38. ^ Garey & Johnson (1979): MP9
  39. ^ Garey & Johnson (1979): ND22, ND23
  40. ^ Garey & Johnson (1979): ND24
  41. ^ Garey & Johnson (1979): MP1
  42. ^ Garey & Johnson (1979): SP16
  43. ^ Garey & Johnson (1979): SP12
  44. ^ Garey & Johnson (1979): ND43
  45. ^ Garey & Johnson (1979): SP13
  46. ^ Lanctot, J. Kevin; Li, Ming; Ma, Bin; Wang, Shaojiu; Zhang, Louxin (2003), "Distinguishing string selection problems", Information and Computation, 185 (1): 41–55, doi:10.1016/S0890-5401(03)00057-9, MR 1994748 
  47. ^ Garey & Johnson (1979): SR10
  48. ^ Garey & Johnson (1979): SR11
  49. ^ Garey & Johnson (1979): SR8
  50. ^ Garey & Johnson (1979): SR20
  51. ^ Malte Helmert, Complexity results for standard benchmark domains in planning, Artificial Intelligence Journal 143(2):219-262, 2003.
  52. ^ Yato, Takauki (2003). "Complexity and Completeness of Finding Another Solution and its Application to Puzzles". CiteSeerX 10.1.1.103.8380 .  Missing or empty |url= (help)
  53. ^ "HASHIWOKAKERO Is NP-Complete". 
  54. ^ Holzer & Ruepp (2007)
  55. ^ Garey & Johnson (1979): GP15
  56. ^ Kölker, Jonas (2012). "Kurodoko is NP-complete". 
  57. ^ Cormode, Graham (2004). The hardness of the lemmings game, or Oh no, more NP-completeness proofs (PDF). 
  58. ^ Light Up is NP-Complete
  59. ^ Friedman, Erich (2012-03-27). "Pearl Puzzles are NP-complete". 
  60. ^ Kaye (2000)
  61. ^ Allan Scott, Ulrike Stege, Iris van Rooij, Minesweeper may not be NP-complete but is hard nonetheless, The Mathematical Intelligencer 33:4 (2011), pp. 5-17.
  62. ^ Garey & Johnson (1979): GT56
  63. ^ a b Sato, Takayuki; Seta, Takahiro (1987). Complexity and Completeness of Finding Another Solution and Its Application to Puzzles (PDF). International Symposium on Algorithms (SIGAL 1987). 
  64. ^ Nukui; Uejima. "ASP-Completeness of the Slither Link Puzzle on Several Grids". 
  65. ^ Kölker, Jonas (2012). "Selected Slither Link Variants are NP-complete". 
  66. ^ A SURVEY OF NP-COMPLETE PUZZLES, Section 23; Graham Kendall, Andrew Parkes, Kristian Spoerer; March 2008. (icga2008.pdf)
  67. ^ Demaine, Eric D.; Hohenberger, Susan; Liben-Nowell, David (July 25–28, 2003). Tetris is Hard, Even to Approximate (PDF). Proceedings of the 9th International Computing and Combinatorics Conference (COCOON 2003). Big Sky, Montana. 
  68. ^ Lim, Andrew (1998), "The berth planning problem", Operations Research Letters, 22 (2–3): 105–110, doi:10.1016/S0167-6377(98)00010-8, MR 1653377 
  69. ^ J. Bonneau, "Bitcoin mining is NP-hard
  70. ^ Garey & Johnson (1979): LO1
  71. ^ Garey & Johnson (1979): p. 48
  72. ^ Garey & Johnson (1979): SR31
  73. ^ Garey & Johnson (1979): GT6
  74. ^ Minimum Independent Dominating Set
  75. ^ Garey & Johnson (1979): GT10
  76. ^ Garey & Johnson (1979): GT49
  77. ^ Garey & Johnson (1979): LO5
  78. ^ https://web.archive.org/web/20150203193923/http://www.meliksah.edu.tr/acivril/max-vol-original.pdf
  79. ^ Peter Downey, Benton Leong, and Ravi Sethi. "Computing Sequences with Addition Chains" SIAM J. Comput., 10(3), 638–646, 1981
  80. ^ D. J. Bernstein, "Pippinger's exponentiation algorithm (draft)
  81. ^ Kashiwabara & Fujisawa (1979); Ohtsuki et al. (1979); Lengauer (1981).
  82. ^ Hurkens, C.; Iersel, L. V.; Keijsper, J.; Kelk, S.; Stougie, L.; Tromp, J. (2007). "Prefix reversals on binary and ternary strings". SIAM J. Discrete Math. 21 (3): 592–611. arXiv:math/0602456 . doi:10.1137/060664252. 
  83. ^ Garey & Johnson (1979): GT48
  84. ^ Garey & Johnson (1979): ND13
  85. ^ Garey & Johnson (1979): SP3
  86. ^ Garey & Johnson (1979): SR33
  87. ^ Bein, W. W.; Larmore, L. L.; Latifi, S.; Sudborough, I. H. (2002-01-01). "Block sorting is hard". International Symposium on Parallel Architectures, Algorithms and Networks, 2002. I-SPAN '02. Proceedings: 307–312. doi:10.1109/ISPAN.2002.1004305. ISBN 0-7695-1579-7. 
  88. ^ Barry A. Cipra, "The Ising Model Is NP-Complete", SIAM News, Vol 33, No 6.
References

General

  • Garey, Michael R.; Johnson, David S. (1979), Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman, ISBN 0-7167-1045-5 . This book is a classic, developing the theory, then cataloguing many NP-Complete problems.
  • Cook, S.A. (1971). "The complexity of theorem proving procedures". Proceedings, Third Annual ACM Symposium on the Theory of Computing, ACM, New York. pp. 151–158. doi:10.1145/800157.805047. 
  • Karp, Richard M. (1972). "Reducibility among combinatorial problems". In Miller, Raymond E.; Thatcher, James W. Complexity of Computer Computations. Plenum. pp. 85–103. 
  • Dunne, P.E. "An annotated list of selected NP-complete problems". COMP202, Dept. of Computer Science, University of Liverpool. Retrieved 2008-06-21. 
  • Crescenzi, P.; Kann, V.; Halldórsson, M.; Karpinski, M.; Woeginger, G. "A compendium of NP optimization problems". KTH NADA, Stockholm. Retrieved 2008-06-21. 
  • Dahlke, K. "NP-complete problems". Math Reference Project. Retrieved 2008-06-21. 

Specific problems

  • Friedman, E (2002). "Pearl puzzles are NP-complete". Stetson University, DeLand, Florida. Retrieved 2008-06-21. 
  • Grigoriev, A; Bodlaender, H L (2007). "Algorithms for graphs embeddable with few crossings per edge". Algorithmica. 49 (1): 1–11. doi:10.1007/s00453-007-0010-x. MR 2344391. 
  • Hartung, S; Nichterlein, A (2012). "NP-Hardness and Fixed-Parameter Tractability of Realizing Degree Sequences with Directed Acyclic Graphs". Springer, Berlin, Heidelberg. Retrieved 2013-01-24. 
  • Holzer, Markus; Ruepp, Oliver (2007). "The Troubles of Interior Design–A Complexity Analysis of the Game Heyawake". Proceedings, 4th International Conference on Fun with Algorithms, LNCS 4475. Springer, Berlin/Heidelberg. pp. 198–212. doi:10.1007/978-3-540-72914-3_18. ISBN 978-3-540-72913-6. 
  • Kaye, Richard (2000). "Minesweeper is NP-complete". Mathematical Intelligencer. 22 (2): 9–15. doi:10.1007/BF03025367.  Further information available online at Richard Kaye's Minesweeper pages.
  • Kashiwabara, T.; Fujisawa, T. (1979). "NP-completeness of the problem of finding a minimum-clique-number interval graph containing a given graph as a subgraph". Proceedings. International Symposium on Circuits and Systems. pp. 657–660. 
  • Ohtsuki, Tatsuo; Mori, Hajimu; Kuh, Ernest S.; Kashiwabara, Toshinobu; Fujisawa, Toshio (1979). "One-dimensional logic gate assignment and interval graphs". IEEE Transactions on Circuits and Systems. 26 (9): 675–684. doi:10.1109/TCS.1979.1084695. 
  • Lengauer, Thomas (1981). "Black-white pebbles and graph separation". Acta Informatica. 16 (4): 465–475. doi:10.1007/BF00264496. 
  • Arnborg, Stefan; Corneil, Derek G.; Proskurowski, Andrzej (1987). "Complexity of finding embeddings in a k-tree". SIAM Journal on Algebraic and Discrete Methods. 8 (2): 277–284. doi:10.1137/0608024. 
  • Cormode, Graham (2004). "The hardness of the lemmings game, or Oh no, more NP-completeness proofs". Proceedings of Third International Conference on Fun with Algorithms (FUN 2004). pp. 65–76. 
External links
  • A compendium of NP optimization problems
  • Graph of NP-complete Problems



Twitter
 
Facebook
 
LinkedIn
 
 

 
 

WhmSoft Moblog
Copyright (C) 2006-2019 WhmSoft
All Rights Reserved