On the Quantum and Classical Complexity of Solving Subtraction Games

Kravchenko, Dmitry; Khadiev, Kamil; Serov, Danil

doi:10.1007/978-3-030-19955-5_20

Cited by 11 publications

(9 citation statements)

References 14 publications

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“…Grover's algorithm has been used to obtain quantum speedups for various problems in combinatorial optimization and computer science (see, for e.g., [16], [17], [19], [22], [35]). Needless to say, graph coloring problems are also not an exception in the literature, and have been attacked using quantum annealing [21], [37], hybrid approaches [6], [36], as well as using Grover search [32], [34], [40].…”

Section: Introductionmentioning

confidence: 99%

A Grover Search-Based Algorithm for the List Coloring Problem

Mukherjee

2022

IEEE Trans. Quantum Eng.

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Section: Introductionmentioning

confidence: 99%

A Grover Search-Based Algorithm for the List Coloring Problem

Mukherjee

2022

IEEE Trans. Quantum Eng.

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“…Nim games are notable games in game theory, and they have similar definitions to subtraction games [17]. Following the definition of subtraction games introduced by Kravchenko et al [18], there are two players, a heap of tokens and a strategy matrix Γ, in a subtraction game. Based on the strategy matrix Γ, two players take away a number of tokens one by one.…”

Section: Introductionmentioning

confidence: 99%

“…In addition, Huang proposed a restricted subtraction game in [19], where a constraint is imposed on the strategy matrix. In the restricted subtraction games, at most one "1" is allowed in each column of the strategy matrix, and the rest is the same as the common subtraction games introduced in [18].…”

Section: Introductionmentioning

confidence: 99%

“…As for the restricted subtraction game, Huang [19] proposed an exact quantum query algorithm to solve it with a query complexity of O(N 3 2 ). The proposed quantum algorithms to solve the common subtraction games and the restricted subtraction games in [18,19] are mainly based on Grover's algorithm [20] and exact Grover's algorithm [21], respectively. As mentioned earlier, there is a subroutine to find the position of an element in a disorder data set.…”

Section: Introductionmentioning

confidence: 99%

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A linear algorithm for the restricted subtraction games

Yang

He²,

Li³

et al. 2022

Front. Phys.

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The subtraction game is a well-known problem in the field of game theory, which is often called a one-heap Nim game. There are two players, a heap of tokens, and a strategy matrix, in this game. It is called a restricted subtraction game if some constraints are imposed on the strategy matrix. The subtraction game could be solved by a classical algorithm with a query complexity no less than O(N2) and computed by an O(N32logN) quantum query algorithm with an error probability ϵ≤1N. The restricted subtraction game proposed by Huang et al. can be computed by an exact quantum algorithm with O(N32) queries. They also proved that the classical exact query complexity is Θ(N2). In this study, we use an array and an adjacency list to replace the strategy matrix and propose another more general subtraction game than the one introduced by Huang et al. Based on dynamic programming and the replaced game strategy, two linear classical query algorithms are designed to solve the restricted subtraction game proposed by Huang and this study, respectively.

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“…Grover's algorithm has been used to obtain quantum speedups for various problems in combinatorial optimization and computer science (see, for e.g., [18,31,16,15,20]). Needless to say, graph coloring problems are also not an exception in the literature, and have been attacked using quantum annealing [33,19], hybrid approaches [32,5], as well as using Grover search [36,30,28].…”

Section: Introductionmentioning

confidence: 99%

A Grover search-based algorithm for the list coloring problem

Mukherjee

2021

Preprint

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Graph coloring is a computationally difficult problem, and currently the best known classical algorithm for k-coloring of graphs on n vertices has runtimes Ω(2 n ) for k ≥ 5. The list coloring problem asks the following more general question: given a list of available colors for each vertex in a graph, does it admit a proper coloring? We propose a quantum algorithm based on Grover search [11] to quadratically speed up exhaustive search. Our algorithm loses in complexity to classical ones in specific restricted cases, but improves exhaustive search for cases where the lists and graphs considered are arbitrary in nature.

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On the Quantum and Classical Complexity of Solving Subtraction Games

Cited by 11 publications

References 14 publications

A Grover Search-Based Algorithm for the List Coloring Problem

A Grover Search-Based Algorithm for the List Coloring Problem

A linear algorithm for the restricted subtraction games

A Grover search-based algorithm for the list coloring problem

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