Journal of Combinatorial Optimization最新文献

In this paper, we consider the following two-machine no-wait flow shop scheduling problem with two competing agents (F2~|~M_1rightarrow M_2,~ M_2,~ p_{ij}^{A} = p,~ notext{- }wait~|~C_{max }^A:~ C_{max }^B~le Q ): Given a set of n jobs (mathcal {J} = { J_1, J_2, ldots , J_n}) and two competing agents A and B. Agent A is associated with a set of (n_A) jobs (mathcal {J}^A = {J_1^A, J_2^A, ldots , J_{n_A}^A}) to be processed on the machine (M_1) first and then on the machine (M_2) with no-wait constraint, and agent B is associated with a set of (n_B) jobs (mathcal {J}^B = {J_1^B, J_2^B, ldots , J_{n_B}^B}) to be processed on the machine (M_2) only, where the processing times for the jobs of agent A are all the same (i.e., (p_{ij}^A = p)), (mathcal {J} = mathcal {J}^A cup mathcal {J}^B) and (n = n_A + n_B). The objective is to build a schedule (pi ) of the n jobs that minimizing the makespan of agent A while maintaining the makespan of agent B not greater than a given value Q. We first show that the problem is polynomial time solvable in some special cases. For the non-solvable case, we present an (O(n log n))-time ((1 + frac{1}{n_A +1}))-approximation algorithm and show that this ratio of ((1 + frac{1}{n_A +1})) is asymptotically tight. Finally, ((1+epsilon ))-approximation algorithms are provided.

In light of the successful investigation of the adjacency matrix, a significant amount of its modification is observed employing numerous topological indices. The matrix corresponding to the well-known first Zagreb index is one of them. The entries of the first Zagreb matrix are (d_{u_i}+d_{u_j}), if (u_i) is connected to (u_j); 0, otherwise, where (d_{u_i}) is degree of i-th vertex. The current work is concerned with the mathematical properties and chemical significance of the spectral radius ((rho _1)) associated with this matrix. The lower and upper bounds of (rho _1) are computed with characterizing extremal graphs for the class of unicyclic graphs and trees. The chemical connection of the first Zagreb spectral radius is established by exploring its role as a structural descriptor of molecules. The isomer discrimination ability of (rho _1) is also explained.

The online graph exploration problem, which was proposed by Kalyanasundaram and Pruhs (Theor Comput Sci 130(1):125–138, 1994), is defined as follows: Given an edge-weighted undirected connected graph and a specified vertex (called the origin), the task of an algorithm is to compute a path from the origin to the origin which contains all the vertices of the given graph. The goal of the problem is to find such a path of minimum weight. At each time, an online algorithm knows only the weights of edges each of which consists of visited vertices or vertices adjacent to visited vertices. Fritsch (Inform Process Lett 168:1006096, 2021) showed that the competitive ratio of an online algorithm is at most three for any unicyclic graph. On the other hand, Brandt et al. (Theor Comput Sci 839:176–185, 2020) showed a lower bound of two on the competitive ratio for any unicyclic graph. In this paper, we showed the competitive ratio of an online algorithm is at most 5/2 for any unicyclic graph.

This paper concerns online portfolio selection problem whose main feature is with no any statistical assumption on future asset prices. Since online portfolio selection aims to maximize the cumulative wealth, most existing online portfolio strategies do not consider risk factors into the model. To enrich the research on online portfolio selection, we introduce the risk factors into the model and propose two novel risk-adjusted online portfolio strategies. More specifically, we first choose several exponential gradient ((text {EG}(eta ))) with different values of parameter (eta ) to build an expert pool. Later, we construct two risk methods to measure performance of each expert. Finally, we calculate the portfolio by the weighted average over all expert advice. We present theoretical and experimental results respectively to analyze the performance of the proposed strategies. Theoretical results show that the proposed strategies not only track the expert with the lowest risk, but also are universal, i.e., they exhibit the same asymptotic average logarithmic growth rate as best constant rebalanced portfolio (BCRP) determined in hindsight. We conduct extensive experiments by using daily stock data collected from the American and Chinese stock markets. Experimental results show the proposed strategies outperform existing online portfolio in terms of the return and risk metrics in most cases.

In this work, we focus on maximizing the stochastic DS decomposition problem. If the constraint is a uniform matroid, we design an adaptive policy, namely Myopic Parameter Conditioned Greedy, and prove its theoretical guarantee (f(varTheta (pi _k))-(1-c_G)g(varTheta (pi _k))ge (1-e^{-1})F(pi ^*_A, varTheta (pi _k)) - G(pi ^*_A,varTheta (pi _k))), where (F(pi ^*_A, varTheta (pi _k)) = mathbb {E}_{varTheta }[f(varTheta (pi ^*_A)) vert varTheta (pi _k)]). When the constraint is a general matroid constraint, we design the Parameter Measured Continuous Conditioned Greedy to return a fractional solution. To round an integer solution from the fractional solution, we adopt the lattice contention resolution and prove that there is a ((b, frac{1-e^{-b}}{b})) lattice CR scheme under a matroid constraint. Additionally, we adopt the pipage rounding to obtain a non-adaptive policy with the theoretical guarantee (F(pi )-(1-c_G)G(pi ) ge (1-e^{-1}) F(pi ^*_A) - G(pi ^*_A) - O(epsilon )) and utlize the ((1,1-e^{-1}))-lattice contention resolution scheme (tau ) to obtain an adaptive solution (mathbb {E}_{tau sim varLambda } [f(tau (varTheta (pi )))- (1-c_G) g(tau (varTheta (pi )))] ge (1-e^{-1})^2F(pi ^*_A,varTheta (pi )) - (1-e^{-1}) G(pi ^*_A,varTheta (pi )) -O(epsilon )). Since any set function can be expressed as the DS decomposition, our framework provides a method for solving the maximization problem of set functions defined on a random variable set.

Göring–Helmberg–Wappler introduced optimization problems regarding embeddings of a graph into a Euclidean space and the first nonzero eigenvalue of the Laplacian of a graph, which are dual to each other in the framework of semidefinite programming. In this paper, we introduce a new graph-embedding optimization problem, and discuss its relation to Göring–Helmberg–Wappler’s problems. We also identify the dual problem to our embedding optimization problem. We solve the optimization problems for distance-regular graphs and the one-skeleton graphs of the (textrm{C}_{60}) fullerene and some other Archimedian solids.

Grey wolf optimizer (GWO) is one of the most popular metaheuristics, and it has been presented as highly competitive with other comparison methods. However, the basic GWO needs some improvement, such as premature convergence and imbalance between exploitation and exploration. To address these weaknesses, this paper develops a hybrid grey wolf optimizer (HGWO), which combines the Halton sequence, dimension learning-based, crisscross strategy, and Cauchy mutation strategy. Firstly, the Halton sequence is used to enlarge the search scope and improve the diversity of the solutions. Then, the dimension learning-based is used for position update to balance exploitation and exploration. Furthermore, the crisscross strategy is introduced to enhance convergence precision. Finally, the Cauchy mutation strategy is adapted to avoid falling into the local optimum. The effectiveness of HGWO is demonstrated by comparing it with advanced algorithms on the 15 benchmark functions in different dimensions. The results illustrate that HGWO outperforms other advanced algorithms. Moreover, HGWO is used to solve eight real-world engineering problems, and the results demonstrate that HGWO is superior to different advanced algorithms.

An injective edge-coloring of a graph G is an edge-coloring of G such that any two edges that are at distance 2 or in a common triangle receive distinct colors. The injective chromatic index of G is the minimum number of colors needed to guarantee that G admits an injective edge-coloring. Ferdjallah, Kerdjoudj and Raspaud showed that the injective chromatic index of every subcubic graph is at most 8, and conjectured that 8 can be improved to 6. Kostochka, Raspaud and Xu further proved that every subcubic graph has the injective chromatic index at most 7, and every subcubic planar graph has the injective chromatic index at most 6. In this paper, we consider the injective edge-coloring of claw-free subcubic graphs. We show that every connected claw-free subcubic graph, apart from two exceptions, has the injective chromatic index at most 5. We also consider the list version of injective edge-coloring and prove that the list injective chromatic index of every claw-free subcubic graph is at most 6. Both results are sharp and strengthen a recent result of Yang and Wu which asserts that every claw-free subcubic graph has the injective chromatic index at most 6.

A Hamiltonian decomposition of a regular graph is a partition of its edge set into Hamiltonian cycles. We consider the second Hamiltonian decomposition problem: for a 4-regular multigraph, find 2 edge-disjoint Hamiltonian cycles different from the given ones. This problem arises in polyhedral combinatorics as a sufficient condition for non-adjacency in the 1-skeleton of the traveling salesperson polytope. We introduce two integer linear programming models for the problem based on the classical Dantzig-Fulkerson-Johnson and Miller-Tucker-Zemlin formulations for the traveling salesperson problem. To enhance the performance on feasible problems, we supplement the algorithm with a variable neighborhood descent heuristic w.r.t. two neighborhood structures and a chain edge fixing procedure. Based on the computational experiments, the Dantzig-Fulkerson-Johnson formulation showed the best results on directed multigraphs, while on undirected multigraphs, the variable neighborhood descent heuristic was especially effective.

Given a strongly connected mixed graph (G=(V,E,A)), where V represents the vertex set, E is the undirected edge set, and A is the directed arc set, (R subseteq E) is a subset of required edges and is divided into p clusters (R_1,R_2,dots ,R_p), and A is a set of required arcs and is partitioned into q clusters (A_1,A_2,ldots ,A_q). Each edge in E and each arc in A are associated with a nonnegative weight and the weight function satisfies the triangle inequality. In this paper we consider two clustered arc routing problems. The first is the Clustered Rural Postman Problem, in which A is empty and the objective is to find a minimum-weight closed walk such that all the edges in R are serviced and the edges in (R_i) ((1le i le p)) are serviced consecutively. The other is the Clustered Stacker Crane Problem, in which R is empty and the goal is to find a minimum-weight closed walk that traverses all the arcs in A and services the arcs in (A_j) ((1le j le q)) consecutively. For both problems, we propose constant-factor approximation algorithms with ratios 13/6 and 19/6, respectively.