Algorithms for Finding Maximal and Maximum Cliques: A Survey

Fakhfakh, Faten; Tounsi, Mohamed; Mosbah, Mohamed; Kacem, Ahmed Hadj

doi:10.1007/978-3-319-76348-4_72

Cited by 4 publications

(3 citation statements)

References 21 publications

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“…[11] proposes a novel branch pruning strategy, which can efficiently reduce the search space by ignoring the search process from the neighbors of the pivot. [44] reviews recently advances in maximal clique enumeration. Based on clique, other cohesive subgraph models are also studied, such as k-core [45], k-truss [46], [47], k-edge connected component [48], [49], [50], and (r, s)-nuclei [51], [52].…”

Section: Related Workmentioning

confidence: 99%

Balanced Clique Computation in Signed Networks: Concepts and Algorithms

Chen¹,

Yuan²,

Lin³

et al. 2022

Preprint

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Clique is one of the most fundamental models for cohesive subgraph mining in network analysis. Existing clique model mainly focuses on unsigned networks. However, in real world, many applications are modeled as signed networks with positive and negative edges. As the signed networks hold their own properties different from the unsigned networks, the existing clique model is inapplicable for the signed networks. Motivated by this, we propose the balanced clique model that considers the most fundamental and dominant theory, structural balance theory, for signed networks. Following the balanced clique model, we study the maximal balanced clique enumeration problem (MBCE) which computes all the maximal balanced cliques in a given signed network. Moreover, in some applications, users prefer a unique and representative balanced clique with maximum size rather than all balanced cliques. Thus, we also study the maximum balanced clique search problem (MBCS) which computes the balanced clique with maximum size. We show that MBCE problem and MBCS problem are both NP-Hard. For the MBCE problem, a straightforward solution is to treat the signed network as two unsigned networks and leverage the off-the-shelf techniques for unsigned networks. However, such a solution is inefficient for large signed networks. To address this problem, in this paper, we first propose a new maximal balanced clique enumeration algorithm by exploiting the unique properties of signed networks. Based on the new proposed algorithm, we devise two optimization strategies to further improve the efficiency of the enumeration. For the MBCS problem, we first propose a baseline solution. To overcome the huge search space problem of the baseline solution, we propose a new search framework based on search space partition. To further improve the efficiency of the new framework, we propose multiple optimization strategies regarding to redundant search branches and invalid candidates. We conduct extensive experiments on large real datasets. The experimental results demonstrate the efficiency, effectiveness and scalability of our proposed algorithms for MBCE problem and MBCS problem.

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Section: Related Workmentioning

confidence: 99%

Balanced Clique Computation in Signed Networks: Concepts and Algorithms

Chen¹,

Yuan²,

Lin³

et al. 2022

Preprint

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“…Trong vài năm trở lại đây, có nhiều công trình nghiên cứu về MCP và các ứng dụng không liên quan đến mạng lưới toàn cầu như: xác định các cấu trúc protein tương đồng [2] -sinh học; theo dõi đa mục tiêu [9] -thị giác máy tính; phân cụm điện não đồ [12] -y học; xếp hạng các trường đại học [13] -giáo dục;... Nhóm tác giả dựa vào công trình khảo sát [10], có thể phân loại các nghiên cứu giải bài toán MCP theo hai nhóm chiến lược tiếp cận:…”

Section: Giới Thiệuunclassified

Tiếp cận Heuristic giải bài toán Clique lớn nhất trên đồ thị đơn vô hướng không trọng số

Phan¹,

Huỳnh²,

Châu³

2021

Chuyên san CNTT-TT

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Bài toán Clique lớn nhất (Maximum Clique Problem) là bài toán tìm tập con lớn nhất của tập đỉnh trong đơnđồ thị vô hướng, sao cho hai đỉnh phân biệt trong nó luôn kề nhau. Đây là bài toán nổi tiếng thuộc lớp NP-complete, đượcứng dụng nhiều trong các lĩnh vực khai thác dữ liệu, phân tích mạng, truy xuất thông tin, y học, giáo dục và nhiều lĩnhvực khác liên quan đến mạng lưới toàn cầu. Có nhiều cách tiếp cận giải bài toán Clique lớn nhất như quy hoạch động,nhánh-cận, heuristic hay meta-heuristic – cho lời giải chính xác hay xấp xỉ. Trong bài báo này, nhóm tác giả phân tíchhai thuật giải tiếp cận heuristic gần đây và đề xuất các heuristic tăng độ chính xác của lời giải cho bài toán Clique lớnnhất. Phần thực nghiệm, nhóm tác giả so sánh chất lượng lời giải của thuật giải đề xuất trên 10 bộ dữ liệu từ DIMACS.

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“…These techniques for biclique enumeration inspire our techniques presented in Section 6.1. [14] reviews recently advances in maximal clique enumeration. Based on clique, other cohesive subgraph models are also studied recently, such as k-core [43], ktruss [9,20], k-edge connected component [52,54,59], (r, s)-nuclei [40,41].…”

Section: Related Workmentioning

confidence: 99%

Efficient Maximal Balanced Clique Enumeration in Signed Networks

Zi¹,

Yuan

Lin

et al. 2020

Proceedings of the Web Conference 2020

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Clique is one of the most fundamental models for cohesive subgraph mining in network analysis. Existing clique model mainly focuses on unsigned networks. In real world, however, many applications are modeled as signed networks with positive and negative edges. As the signed networks hold their own properties different from the unsigned networks, the existing clique model is inapplicable for the signed networks. Motivated by this, we propose the balanced clique model that considers the most fundamental and dominant theory, structural balance theory, for signed networks, and study the maximal balanced clique enumeration problem which computes all the maximal balanced cliques in a given signed network. We show that the maximal balanced clique enumeration problem is NP-Hard. A straightforward solution for the maximal balanced clique enumeration problem is to treat the signed network as two unsigned networks and leverage the off-the-shelf techniques for unsigned networks. However, such a solution is inefficient for large signed networks. To address this problem, in this paper, we first propose a new maximal balanced clique enumeration algorithm by exploiting the unique properties of signed networks. Based on the new proposed algorithm, we devise two optimization strategies to further improve the efficiency of the enumeration. We conduct extensive experiments on large real and synthetic datasets. The experimental results demonstrate the efficiency, effectiveness and scalability of our proposed algorithms.

show abstract

Algorithms for Finding Maximal and Maximum Cliques: A Survey

Cited by 4 publications

References 21 publications

Balanced Clique Computation in Signed Networks: Concepts and Algorithms

Balanced Clique Computation in Signed Networks: Concepts and Algorithms

Tiếp cận Heuristic giải bài toán Clique lớn nhất trên đồ thị đơn vô hướng không trọng số

Efficient Maximal Balanced Clique Enumeration in Signed Networks

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