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In computer science and artificial intelligence, combinatorial search studies search algorithms for solving instances of problems that are believed to
Combinatorial_search
Subfield of mathematical optimization
Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, where the
Combinatorial_optimization
The Symposium on Combinatorial Search (SoCS) in an international conference aimed at bringing together researchers and all others interested in all fields
Symposium on Combinatorial Search
Symposium_on_Combinatorial_Search
Class of search algorithms
a combinatorial search instance may consist of the goal state itself, or of a path from some initial state to the goal state. In state-space search, a
State-space_search
Any algorithm which solves the search problem
financial, or military strategy planning. This kind of problem — combinatorial search — has been extensively studied in the context of artificial intelligence
Search_algorithm
Search algorithm
its search tree. It is an adversarial search algorithm used commonly for machine playing of two-player combinatorial games (Tic-tac-toe, Chess, Connect 4
Alpha–beta_pruning
Algorithm for finding shortest paths
Algorithm versus Uniform Cost Search or a Case Against Dijkstra's Algorithm. Proc. 4th Int'l Symp. on Combinatorial Search. Archived from the original on
Dijkstra's_algorithm
Graph exploring search algorithm
A* search algorithm is an example of a best-first search algorithm, as is B*. Best-first algorithms are often used for path finding in combinatorial search
Best-first_search
algorithm Approximation algorithm Best and worst cases Big O notation Combinatorial search Competitive analysis Computability theory Computational complexity
List of algorithm general topics
List_of_algorithm_general_topics
Concept of social inter-connectedness
Archived 2014-12-10 at the Wayback Machine", Fourth Annual Symposium on Combinatorial Search, 2011 Memorable quotes from Six Degrees of Separation. Accessed Nov
Six_degrees_of_separation
Algorithm used for pathfinding and graph traversal
algorithm. A* achieves better performance by using heuristics to guide its search. The A* algorithm terminates once it finds the shortest path to a specified
A*_search_algorithm
Set of objects whose state must satisfy limits
exhibit high complexity, requiring a combination of heuristics and combinatorial search methods to be solved in a reasonable time. Constraint programming
Constraint satisfaction problem
Constraint_satisfaction_problem
Topics referred to by the same term
dictionary. Lookahead or Look Ahead may refer to: A parameter of some combinatorial search algorithms, describing how deeply the graph representing the problem
Lookahead
Topics referred to by the same term
involved in inhibiting the JAK-STAT signaling pathway Symposium on Combinatorial Search, international computer science conference System on a chip, an integrated
Socs
Algorithm
strategy in a sum game of a set of combinatorial games. Branch and bound Berliner, Hans (1979). "The B* Tree Search Algorithm. A Best-First Proof Procedure"
B*
Search algorithm used in sorted arrays
In computer science, binary search, also known as half-interval search, logarithmic search, or binary chop, is a search algorithm that finds the position
Binary_search
determine how well a given combinatorial construct reflects the observed data, or to search for a suitable combinatorial construct that does fit the
Combinatorial_data_analysis
Computer science pathfinding concept
"Common Misconceptions Concerning Heuristic Search". Proceedings of the Third Annual Symposium on Combinatorial Search (SoCS). Archived from the original on
Admissible_heuristic
Reverse-search algorithms are a class of algorithms for generating all objects of a given size, from certain classes of combinatorial objects. In many
Reverse-search_algorithm
American computer scientist (born 1945)
to have potential as a means to solve several other large-scale combinatorial search problems. Adleman is widely referred to as the Father of DNA Computing
Leonard_Adleman
Branch of game theory about two-player sequential games with perfect information
Combinatorial game theory is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information
Combinatorial_game_theory
Problem-solving technique and algorithmic paradigm
quickly as the size of the problem increases (§Combinatorial explosion). Therefore, brute-force search is typically used when the problem size is limited
Brute-force_search
Optimization technique
problems to combinatorial optimization or combinations thereof. In combinatorial optimization, an optimal solution is sought over a discrete search-space.
Metaheuristic
Algorithm to find Euclidean shortest paths
Algorithms. Proceedings of the Eighth International Symposium on Combinatorial Search. A. Nash. Any-Angle Path Planning. PhD thesis, Department of Computer
Any-angle_path_planning
eliminate symmetries and reduce the search space size. Symmetries in a combinatorial problem increase the size of the search space and therefore, time is wasted
Symmetry-breaking_constraints
Overview of and topical guide to combinatorics
geometry Phylogenetics History of combinatorics Combinatorial principles Trial and error, brute-force search, bogosort, British Museum algorithm Pigeonhole
Outline_of_combinatorics
Problem of finding the best feasible solution
constraints. In a discrete optimization problem, such as combinatorial optimization, the search space could consist of a finite set of permutations, combinations
Optimization_problem
Variation of the minimax algorithm
iterative search is about to score the i {\displaystyle i} th child of a chance node with N {\displaystyle N} equally likely children, that search has computed
Expectiminimax
Statistical procedure of testing by group
In statistics and combinatorial mathematics, group testing is any procedure that breaks up the task of identifying objects into tests on groups of items
Group_testing
Formatting to make code or markup easier to read
"GRINDEF" (i.e. 'grind function') program (c. 1967), which used combinatorial search with pruning, to format LISP programs. Early versions operated on
Pretty-printing
Type of heuristic in path-finding problems
"Common Misconceptions Concerning Heuristic Search". Proceedings of the Third Annual Symposium on Combinatorial Search (SoCS). Archived from the original on
Consistent_heuristic
Decision rule used for minimizing the possible loss for a worst-case scenario
is a decision rule used in artificial intelligence, decision theory, combinatorial game theory, statistics, and philosophy for minimizing the possible
Minimax
Intelligence in machines
insufficient for solving large reasoning problems because they experienced a "combinatorial explosion", meaning they become exponentially slower as the problems
Artificial_intelligence
Simplified example problem used for research or exposition
ISBN 978-0-13-604259-4. Korf, Richard E. (2012). "Research Challenges in Combinatorial Search". In Hoffmann, Jörg; Selman, Bart (eds.). Proceedings of the Twenty-Sixth
Toy_problem
Meta-algorithmic technique to choose an algorithm
v30i1.10440. S2CID 6676831. Kotthoff, Lars. "Algorithm selection for combinatorial search problems: A survey." Data Mining and Constraint Programming. Springer
Algorithm_selection
Sequence of locally optimal choices
reconsider past choices. Greedy algorithms are often used to solve combinatorial optimization problems. If an optimization problem only depends on the
Greedy_algorithm
Technique for finding an extremum of a function
The golden-section search is a technique for finding an extremum (minimum or maximum) of a function inside a specified interval. For a strictly unimodal
Golden-section_search
Austrian mathematician (1942–2023)
CD-player, by Martin Aigner, Ehrhard Behrends, 2008, ISBN 3-8348-0416-9 Combinatorial search. Teubner, Stuttgart 1988, ISBN 3-519-02109-9 Graphentheorie. Eine
Martin_Aigner
Population-based search algorithm
algorithm performs a kind of neighbourhood search combined with global search, and can be used for both combinatorial optimization and continuous optimization
Bees_algorithm
Mathematical modelling alogorithm
models consideration that is becoming more and more popular is a combinatorial search that is either limited or full. This approach has some advantages
Group_method_of_data_handling
Type of quantum information processing
Adiabatic quantum computation solves satisfiability problems and other combinatorial search problems, particularly such problems that can be formulated as the
Adiabatic_quantum_computation
Multiple interactions and regulation of life forms with their environment
energetics are expected substrates for molecular information and large combinatorial search spaces. Constructor logic of self-reproduction: closed compartments
Living_systems
Software testing method
In computer science, all-pairs testing or pairwise testing is a combinatorial method of software testing that, for each pair of input parameters to a
All-pairs_testing
Heuristic search algorithm for evaluating game trees
In computer science, Monte Carlo tree search (MCTS) is a heuristic tree search algorithm for some kinds of decision processes, most notably those employed
Monte_Carlo_tree_search
Local search algorithm
touched because they are sacred. Tabu search is a metaheuristic algorithm that can be used for solving combinatorial optimization problems (problems where
Tabu_search
Mathematical game
1016/S0304-3975(99)00082-1. Nathan Bullock Domineering:Solving Large Combinatorial Search Spaces M.Sc. thesis, 2002 Uiterwijk, J. W. H. 11x11 Domineering Is
Domineering
Task of computing complete subgraphs
2009-12-17. Karp, Richard M. (1976), "Probabilistic analysis of some combinatorial search problems", in Traub, J. F. (ed.), Algorithms and Complexity: New
Clique_problem
Class of computational problems
answer given x". Search problems frequently occur in graph theory and combinatorial optimization, e.g. searching for matchings, optional cliques, and stable
Search_problem
Numerical optimization method
Random search (RS) is a family of numerical optimization methods that do not require the gradient of the optimization problem, and RS can hence be used
Random_search
2011 book about sudoku
puzzles using Burnside's lemma in group theory. Chapter six looks at combinatorial search techniques for finding small systems of givens that uniquely define
Taking_Sudoku_Seriously
Metaheuristic method for optimization problems
Variable neighborhood search (VNS), proposed by Mladenović & Hansen in 1997, is a metaheuristic method for solving a set of combinatorial optimization and
Variable_neighborhood_search
Numbering of combinations of items
In mathematics, and in particular in combinatorics, the combinatorial number system of degree k (for some positive integer k), also referred to as combinadics
Combinatorial_number_system
Software for solving constraint satisfaction problems
programming community. Minion has been applied in academic work on combinatorial search, scheduling and test generation, and is available to other environments
Minion_(solver)
Metaheuristic commonly used for optimization problems
greedy randomized adaptive search procedure (also known as GRASP) is a metaheuristic algorithm commonly applied to combinatorial optimization problems. GRASP
Greedy randomized adaptive search procedure
Greedy_randomized_adaptive_search_procedure
Optimization algorithm
In optimization, line search is a basic iterative approach to find a local minimum x ∗ {\displaystyle \mathbf {x} ^{*}} of an objective function f : R
Line_search
Collatz conjecture Combination Combinatorial design Combinatorial number system Combinatorial optimization Combinatorial search Constraint satisfaction problem
Index of combinatorics articles
Index_of_combinatorics_articles
Benefits of Randomly Adjusting Anytime Weighted A*". Proceedings of the Fourteenth International Symposium on Combinatorial Search. Retrieved 21 July 2021.
Anytime_A*
Local Search, Wiley Encyclopedia of Operations Research and Management Science, Wiley, 2010 Voudouris, C, Guided local search for combinatorial optimisation
Guided_local_search
Algorithmic optimization method
In the design and analysis of algorithms for combinatorial optimization, parametric search is a technique invented by Nimrod Megiddo in 1983 for transforming
Parametric_search
Optimization algorithm
In operations research, cuckoo search is an optimization algorithm developed by Xin-She Yang and Suash Deb in 2009. It has been shown to be a special case
Cuckoo_search
Family of numerical optimization methods
Pattern search (also known as direct search, derivative-free search, or black-box search) is a family of numerical optimization methods that does not require
Pattern_search_(optimization)
Optimization by removing non-optimal solutions to subproblems
optimal solution. It is an algorithm design paradigm for discrete and combinatorial optimization problems, as well as mathematical optimization. A branch-and-bound
Branch_and_bound
multiplication Combinatorial optimization: optimization problems where the set of feasible solutions is discrete Greedy randomized adaptive search procedure
List_of_algorithms
Protocol for distributed hash table
files over the network within a searchable database. e.g. P2P file transfer clients. Large scale combinatorial searches: Keys being candidate solutions
Chord_(peer-to-peer)
Method for problem solving in optimization
In computer science, local search is a heuristic method for solving computationally hard optimization problems. Local search can be used on problems that
Local_search_(optimization)
Specific sequence of moves in a game
other games. It also is a useful term used when describing computer tree-search algorithms (for example minimax) for playing games such as Go or Chess.
Variation_(game_tree)
Properties of 2D or 3D digital images that correspond to classic topological properties
grid cell topology, which could be considered as a link to classic combinatorial topology, appeared in the book of Pavel Alexandrov and Heinz Hopf, Topologie
Digital_topology
Number Partitioning". Proceedings of the International Symposium on Combinatorial Search. 1: 71–72. doi:10.1609/socs.v1i1.18172. S2CID 45875088. Walter, Rico
Multiway_number_partitioning
Algorithm analysis method
that make it very well-suited to probabilistic analysis. A number of local search algorithms have bad worst-case running times but perform well in practice
Smoothed_analysis
Portuguese-American computer scientist
Artificial Intelligence Classic Paper Award for their 1998 paper Boosting Combinatorial Search through Randomization, which provided "significant contributions
Carla_Gomes
Combinatorial game theory concept to represent all possible game states
In the context of combinatorial game theory, a game tree is a graph representing all possible game states within a sequential game that has perfect information
Game_tree
Computational problem in graph theory
difficult as the dimension number increases and the search space suffers a serious combinatorial explosion. Some techniques for determining the upper
Snake-in-the-box
Mathematical optimization technique
mathematical optimization, neighborhood search is a technique that tries to find good or near-optimal solutions to a combinatorial optimisation problem by repeatedly
Very large-scale neighborhood search
Very_large-scale_neighborhood_search
Searching for patterns in text
approach to suffix automata: Fast extended string matching" (PDF). Combinatorial Pattern Matching. Lecture Notes in Computer Science. Vol. 1448. Springer
String-searching_algorithm
Optimization algorithms using quantum computing
problem is formulated as a minimization of a target functional. For combinatorial optimization problems no proven exponential speed up has ever been found
Quantum optimization algorithms
Quantum_optimization_algorithms
NP-hard problem in combinatorial optimization
general heuristics devised for combinatorial optimization such as genetic algorithms, simulated annealing, tabu search, ant colony optimization, river
Travelling_salesman_problem
Study of mathematical algorithms for optimization problems
possible realizations of the uncertainties defined by an uncertainty set. Combinatorial optimization is concerned with problems where the set of feasible solutions
Mathematical_optimization
Nash equilibrium of a bimatrix game algorithm
Lemke and J. T. Howson. It is said to be "the best known among the combinatorial algorithms for finding a Nash equilibrium", although more recently the
Lemke–Howson_algorithm
Algorithmic paradigm for constraint satisfaction or enumeration problems
convenient technique for parsing, for the knapsack problem and other combinatorial optimization problems. It is also the program execution strategy used
Backtracking
Two-person zero-sum game
value estimates mitigate combinatorial explosion while preserving optimality in some cases. Hohzaki, Ryusuke (2016). "Search Games: Literature and Survey"
Search_game
American physicist
optimization algorithm (QAOA) for finding approximate solutions to combinatorial search problems, which as of 2024 was viewed as a leading candidate to run
Edward_Farhi
Branch of computer science
(3D reconstruction). The main branches of computational geometry are: Combinatorial computational geometry, also called algorithmic geometry, which deals
Computational_geometry
Algorithm for linear programming
Simplex Pivoting Rules and Complexity Theory", Integer Programming and Combinatorial Optimization, Lecture Notes in Computer Science, vol. 17, pp. 13–24
Simplex_algorithm
Application of metaheuristic search techniques to software engineering
optimization problems, for example, assigning people to tasks (a typical combinatorial optimization problem). white-box problems where operations on source
Search-based software engineering
Search-based_software_engineering
Mathematical optimization problem restricted to integers
A Tutorial on Integer Programming Conference Integer Programming and Combinatorial Optimization, IPCO The Aussois Combinatorial Optimization Workshop
Integer_programming
String in combinatorial math
In combinatorial mathematics, a superpermutation on n symbols is a string that contains each permutation of n symbols as a substring. While trivial superpermutations
Superpermutation
Methods in numerical computation
Rosenbrock search is also used to initialize some root-finding routines, such as fzero (based on Brent's method) in Matlab. Rosenbrock search is a form
Rosenbrock_methods
Israeli cryptographer and cryptanalyst
Composite Problems, with Applications to Cryptanalysis, Knapsacks, and Combinatorial Search Problems". In Safavi-Naini, Reihaneh; Canetti, Ran (eds.). Advances
Orr_Dunkelman
Mathematical models of strategic interactions
game theory include algorithmic game theory, behavioral game theory, combinatorial game theory, evolutionary game theory, and quantum game theory. In 1994
Game_theory
Enhancement of Alpha–Beta game tree search
Principal variation search (sometimes equated with the practically identical NegaScout) is a negamax algorithm that can be faster than alpha–beta pruning
Principal_variation_search
Classification of algorithm
(2012). "The disjoint paths problem in quadratic time". Journal of Combinatorial Theory. Series B. 102 (2): 424–435. doi:10.1016/j.jctb.2011.07.004.
Galactic_algorithm
Sequential model-based optimization of expensive black-box functions
1007/3-540-61723-X_982. Rubinstein, Reuven Y. (1999). "The Cross-Entropy Method for Combinatorial and Continuous Optimization". Methodology and Computing in Applied Probability
Bayesian_optimization
Numerical optimization algorithm
maximum of an objective function in a multidimensional space. It is a direct search method (based on function comparison) and is often applied to nonlinear
Nelder–Mead_method
algorithm is an efficient method for computers to construct optimal binary search trees and alphabetic Huffman codes, in linearithmic time. It is named after
Garsia–Wachs_algorithm
Books about algorithms by Donald Knuth
Combinatorial searching (continued) Chapter 8 – Recursion Volume 5 – Syntactic Algorithms Chapter 9 – Lexical scanning (also includes string search and
The Art of Computer Programming
The_Art_of_Computer_Programming
Auctioning of sponsored search engine results
A sponsored search auction (SSA), also known as a keyword auction, is an indispensable part of the business model of modern web hosts. It refers to results
Sponsored_search_auction
Game whose outcome can be correctly predicted
full information and no element of chance; solving such a game may use combinatorial game theory or computer assistance. A two-player game can be solved
Solved_game
Algorithmic determination of legal moves in a strategy game engine
possible positions grow exponentially with search depth, move generation has a major effect on speed and search. The field developed alongside early chess
Move_generation
Substance produced in the digestive system of sperm whales
Weifan; Wolschann, Peter; Buchbauer, Gerhard; Tropsha, Alexander (2004). "Combinatorial QSAR of Ambergris Fragrance Compounds" (PDF). Journal of Chemical Information
Ambergris
Russian-born American mathematician
Springs as of 2026. The journal covers problems in discrete, convex, and combinatorial geometry, as well as related areas. Geombinatorics is indexed in Zentralblatt
Alexander_Soifer
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COMBINATORIAL SEARCH
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