Journal of Combinatorial Optimization最新文献

In this work, we consider the Submodular Maximization under Knapsack ((textsf{SMK})) constraint problem over the ground set of size n. The problem recently attracted a lot of attention due to its applications in various domains of combinatorial optimization, artificial intelligence, and machine learning. We improve the approximation factor of the fastest deterministic algorithm from (6+epsilon ) to (5+epsilon ) while keeping the best query complexity of O(n), where (epsilon >0) is a constant parameter. Our technique is based on optimizing the performance of two components: the threshold greedy subroutine and the building of two disjoint sets as candidate solutions. Besides, by carefully analyzing the cost of candidate solutions, we obtain a tighter approximation factor.

In the field of optimization algorithms, nature-inspired techniques have garnered attention for their adaptability and problem-solving prowess. This research introduces the Arctic Fox Algorithm (AFA), an innovative optimization technique inspired by the adaptive survival strategies of the Arctic fox, designed to excel in dynamic and complex optimization landscapes. Incorporating gradient flow dynamics, stochastic differential equations, and probability distributions, AFA is equipped to adjust its search strategies dynamically, enhancing both exploration and exploitation capabilities. Through rigorous evaluation on a set of 25 benchmark functions, AFA consistently outperformed established algorithms particularly in scenarios involving high-dimensional and multi-modal problems, demonstrating faster convergence and improved solution quality. Application of AFA to real-world problems, including wind farm layout optimization and financial portfolio optimization, highlighted its ability to increase energy outputs by up to 15% and improve portfolio Sharpe ratios by 20% compared to conventional methods. These results showcase AFA’s potential as a robust tool for complex optimization tasks, paving the way for future research focused on refining its adaptive mechanisms and exploring broader applications.

In order to maximize full-view coverage of moving targets in Camera Sensor Networks (CSNs), a novel method known as “group set cover” is presented in this research. Choosing the best camera angles and placements to accomplish full-view coverage of the moving targets is one of the main focuses of the research in CSNs. Discretize the target into multiple views of [0, 2(pi )], use a set of views of targets to represent the sensing direction of the camera sensor, and use a group set of views of targets to represent the position of the camera sensor. The total number of targets in a dynamic time window that is visible in full view is calculated. A mixed integer linear programming formulation is employed, which is then approximated using a random rounding method. This approximation approach offers a global estimation of local optimality, particularly for non-submodular optimization problems. Two methods for maximizing overall full-view coverage within a dynamic time window are proposed TSC-FTC-DTW and FTC-TW-DTW. Finally, the proposed methods are verified through experiments.

The neighbor-connectivity of a graph G, denoted by (kappa _{NB}(G)), is the least number of vertices such that removing their closed neighborhoods from G results in a graph that is empty, complete, or disconnected. In the paper, we show that for any graph G of order n, (kappa _{NB}(G)le lceil sqrt{2n} rceil -2). We pose a conjecture that (kappa _{NB}(G)le lceil sqrt{n} rceil -1) for a graph G of order n. For supporting it, we show that the conjecture holds for any triangle-free graphs, Cartesian, direct, lexicographic product of any two graphs.

This paper studies a due-window assignment scheduling problem with deterioration effects on a single-machine. Under different due-window assignment, i.e., the due-window of a job without any restriction, our goal is to make a decision on the optimal due-window and sequence of all jobs to minimize the weighted sum of earliness and tardiness, number of early and delayed, due-window starting time and size. We present properties of the optimal solutions, for some special cases, we prove that the problem can be solved in polynomial time. For the general case, we present a lower bound and an upper bound (i.e., a heuristic algorithm), then a branch-and-bound algorithm is proposed.

A k-edge coloring (varphi ) of a graph G is injective if (varphi (e_1)ne varphi (e_3)) for any three consecutive edges (e_1, e_2) and (e_3) of a path or a triangle. The injective chromatic index (chi _i'(G)) of G is the smallest k such that G admits an injective k-edge coloring. By discharging method, we demonstrate that any graph with maximum degree (Delta le 5) has (chi _i'(G)le 12) (resp. 13) if its maximum average degree is less than (frac{20}{7}) (resp. 3), which improves the results of Zhu (2023).

We study the non-submodular maximization problem, whose objective function can be expressed as the Difference between two Set (DS) functions or the Ratio between two Set (RS) functions. For the cardinality-constrained and unconstrained DS maximization problems, we present several deterministic algorithms and our analysis shows that the algorithms can provide provable approximation guarantees. As an application, we manage to derive an improved approximation bound for the DS minimization problem under certain conditions compared with existing results. As for the RS maximization problem, we show that there exists a polynomial-time reduction from the approximation of RS maximization to the approximation of DS maximization. Based on this reduction, we derive the first approximation bound for the cardinality-constrained RS maximization problem. We also devise algorithms for the unconstrained problem and analyze their approximation guarantees. By applying our results to the problem of optimizing the ratio between two supermodular functions, we give an answer to the question posed by Bai et al. (in Proceedings of The 33rd international conference on machine learning (ICML), 2016). Moreover, we give an example to illustrate that whether the set function is normalized has an effect on the approximability of the RS optimization problem.

A network for the transportation of supplies can be described as a rooted tree with a weight of a degree of congestion for each edge. We take the sum of root-leaf distance (SRD) on a rooted tree as the whole degree of congestion of the tree. Hence, we consider the SRD interdiction problem on trees with cardinality constraint by upgrading edges, denoted by (SDIPTC). It aims to maximize the SRD by upgrading the weights of N critical edges such that the total upgrade cost under some measurement is upper-bounded by a given value. The relevant minimum cost problem (MCSDIPTC) aims to minimize the total upgrade cost on the premise that the SRD is lower-bounded by a given value. We develop two different norms including weighted (l_infty ) norm and weighted bottleneck Hamming distance to measure the upgrade cost. We propose two binary search algorithms within O((nlog n)) time for the problems (SDIPTC) under the two norms, respectively. For problems (MCSDIPTC), we propose two binary search algorithms within O((N n^2)) and O((n log n)) under weighted (l_infty ) norm and weighted bottleneck Hamming distance, respectively. These problems are solved through their subproblems (SDIPT) and (MCSDIPT), in which we ignore the cardinality constraint on the number of upgraded edges. Finally, we design numerical experiments to show the effectiveness of these algorithms.

Planar hypergraphs are widely used in several applications, including VLSI design, metro maps, information visualisation, and databases. The minimum ( s-t ) hypercut problem in a weighted hypergraph is to find a partition of the vertices into two nonempty sets, S and ( overline{S} ), with (sin S) and (tin overline{S}) that minimizes the total weight of hyperedges that have at least two endpoints in two different sets. In the present study, we propose an approach that effectively solves the minimum ( s-t ) hypercut problem in (s, t)-planar hypergraphs. The method proposed demonstrates polynomial time complexity, providing a significant advancement in solving this problem. The modelling example shows that the proposed strategy is effective at obtaining balanced bipartitions in VLSI circuits.

Social-media platforms have created new ways for individuals to keep in touch with others, share their opinions and join the discussion on different issues. Traditionally studied by social science, opinion dynamic has attracted the attention from scientists in other fields. The formation and evolution of opinions is a complex process affected by the interplay of different elements that incorporate peer interaction in social networks and the diversity of information to which each individual is exposed. In addition, supplementary information can have an important role in driving the opinion formation and evolution. And due to the character of online social platforms, people can easily end an existing follower-followee relationship or stop interacting with a friend at any time. Taking a step in this direction, we propose the OG–IC model which considers the dynamic of both opinion and relationship in this paper. It not only considers the direct influence of friends but also highlights the indirect effect of group when individuals are exposed to new opinions. And it allows nodes which represent users of social networks to slightly adjust their own opinion and sometimes redefine friendships. A novel problem in social network whose purpose is simultaneously maximizing both the diversity of supplementary information that individuals access to and the influence of supplementary information on individual’s existing opinion is formulated. This problem is proved to be NP-hard and its objective function is neither submodular nor supermodular. However, an algorithm with approximate ratio guarantee is designed based on the sandwich framework. And the effectiveness of our algorithm is experimentally demonstrated on both synthetic and real-world data sets.