A Grover Search-Based Algorithm for the List Coloring Problem

Mukherjee, Sayan

doi:10.1109/tqe.2022.3151137

Cited by 8 publications

(2 citation statements)

References 38 publications

(28 reference statements)

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“…In recent years, quantum algorithms have received considerable attention from researchers, [1,2] attracted by their unique properties such as superposition, [3] interference, [4] and entanglement, [5] which enable exponential or square order speedups compared to classical algorithms. Numerous studies have explored quantum algorithms, [1,2,[6][7][8][9][10][11][12][13][14][15] highlighting their potential for solving various computational problems.…”

Section: Introductionmentioning

confidence: 99%

Quantum algorithm for minimum dominating set problem with circuit design

Zhang 张,

Wang 王,

Liu 刘

et al. 2024

Chinese Phys. B

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In recent years, with the development of quantum computing, using quantum algorithms to solve various problems has attracted widespread attention. Researchers are particularly interested in using the acceleration properties of quantum algorithms to solve NP-complete problems. This paper focuses on the well-known NP-complete problem of finding the minimum dominating set in undirected graphs. To expedite the search process, a quantum algorithm employing Grover’s search is proposed. However, a challenge arises from the unknown number of solutions for the minimum dominating set, rendering direct usage of the original Grover’s search impossible. Thus, a swap test method is introduced to ascertain the number of iterations required. The oracle, diffusion operators, and swap test are designed with achievable quantum gates. The query complexity is O(1.414 n ) and the space complexity is O(n). To validate the proposed approach, qiskit software package is employed to simulate the quantum circuit, yielding the anticipated results.

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Section: Introductionmentioning

confidence: 99%

Quantum algorithm for minimum dominating set problem with circuit design

Zhang 张,

Wang 王,

Liu 刘

et al. 2024

Chinese Phys. B

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“…This algorithm is capable of finding optimal list coloring for graphs with only up to 70 vertices. A grover search based quantum algorithm was proposed by Sayan Mukherjee in 2021 (6) . This algorithm works better in finding list chromatic number of graphs with limited vertices as for large-sized graphs, the time complexity of the algorithm will be increased.…”

Section: Introductionmentioning

confidence: 99%

List Coloring Problem: A Heuristic Approach

Srivastava,

Bansal,

Thapar

2023

IJST

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Background/Objectives: List coloring problem is one of the most important generalizations of well-known graph coloring problem. List coloring of a graph is a problem of assigning colors to all vertices of the graph from a pre-defined list of colors for every vertex in such a way that no two adjacent vertices share the same color. In this process, the highest color assigned to a vertex is called span. The objective of the list coloring problem is to minimize this span. Methods: In this study, two heuristic methods are proposed to solve this problem namely: a greedy randomize adaptive search heuristic and a simple greedy heuristic. Findings: Computational experiments on randomly generated graphs show that both the proposed heuristics are capable of obtaining optimal results. It is also observed that greedy randomize adaptive search heuristic performed well as compared to the other one. Comparison with other state-of-art algorithms reveals that both the proposed heuristics have obtained better results for larger graphs in a reasonable time. Novelty: The origin of list coloring problem is very old, still its solving procedures are limited to mostly exact algorithms. Moreover, there is no heuristic available for LCP for general graphs having vertex size more than 150. This paper is an attempt to develop heuristics/metaheuristics for solving this problem for larger graphs in a reasonable time which is not possible with exact methods.

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