2014/08/19 by Jincheng Mei, Kang Zhao, Mei, Jincheng +3
Computer Science · #Advanced Graph Theory Research #Complexity and Algorithms in Graphs #Cryptography and Data Security #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1408.4389
openalex publication_date 2014/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
With the extensive application of submodularity, its generalizations are constantly being proposed. However, most of them are tailored for special problems. In this paper, we focus on quasi-submodularity, a universal generalization, which satisfies weaker properties than submodularity but still enjoys favorable performance in optimization. Similar to the diminishing return property of submodularity, we first define a corresponding property called the \em single sub-crossing, then we propose two algorithms for unconstrained quasi-submodular function minimization and maximization, respectively. The proposed algorithms return the reduced lattices in O(n) iterations, and guarantee the objective function values are strictly monotonically increased or decreased after each iteration. Moreover, any local and global optima are definitely contained in the reduced lattices. Experimental results verify the effectiveness and efficiency of the proposed algorithms on lattice reduction.