Journal of Combinatorial Optimization最新文献

Given a bipartite graph G, the Bicluster Editing problem asks for the minimum number of edges to insert or delete in G so that every connected component is a bicluster, i.e. a complete bipartite graph. This has several applications, including in bioinformatics and social network analysis. In this work, we study the parameterized complexity under the natural parameter k, which is the number of allowed modified edges. We first show that one can obtain a kernel with 4.5k vertices, an improvement over the previously known quadratic kernel. We then propose an algorithm that runs in time (O^*(2.581^k)). Our algorithm has the advantage of being conceptually simple and should be easy to implement.

Let G be a k-uniform hypergraph with vertex set [n] and edge set E(G), where (kge 2). For (iin [n]), (d_i) denotes the degree of vertex i in G. The ABC spectral radius of G is

We give tight lower and upper bounds for the ABC spectral radius, and determine the maximum ABC spectral radii of uniform hypertrees, uniform non-hyperstar hypertrees and uniform non-power hypertrees of given size, as well as the maximum ABC spectral radii of uniform unicyclic hypergraphs and linear uniform unicyclic hypergraphs of given size, respectively. We also characterize those uniform hypergraphs for which the maxima for the ABC spectral radii are actually attained in all cases.

A neural network accelerated optimization method for FPGA hardware platform is proposed. The method realizes the optimized deployment of neural network algorithms for FPGA hardware platforms from three aspects: computational speed, flexible transplantation, and development methods. Replacing multiplication based on Mitchell algorithm not only breaks through the speed bottleneck of neural network hardware acceleration caused by long multiplication period, but also makes the parallel acceleration of neural network algorithm get rid of the dependence on the number of hardware multipliers in FPGA, which can give full play to the advantages of FPGA parallel acceleration and maximize the computing speed. Based on the configurable strategy of neural network parameters, the number of network layers and nodes within layers can be adjusted according to different logical resource of FPGA, improving the flexibility of neural network transplantation. The adoption of HLS development method overcomes the shortcomings of RTL method in designing complex neural network algorithms, such as high difficulty in development and long development cycle. Using the Cyclone V SE 5CSEBA6U23I7 FPGA as the target device, a parameter configurable BP neural network was designed based on the proposed method. The usage of logical resources such as ALUT, Flip-Flop, RAM, and DSP were 39.6%, 40%, 56.9%, and 18.3% of the pre-optimized ones, respectively. The feasibility of the proposed method was verified using MNIST digital recognition and facial recognition as application scenarios. Compare to pre-optimization, the test time of MNIST number recognition is reduced to 67.58%, and the success rate was lost 0.195%. The test time for facial recognition applications was reduced to 69.571%, and the success rate of combining LDA algorithm was lost within 4%.

This paper tackles the two-machine chain-reentrant flow shop scheduling problem with the no-wait constraint; we assume that each job passes from the first machine to the second and returns back to the first machine in order to execute its last operation. The objective is to minimize the makespan. In this work, we prove that the symmetric case of this problem, which is proven to be (mathcal NP)-hard in the strong sense, remains (mathcal NP)-hard. Then we provide two polynomial subproblems. For the main problem’s resolution, we propose two new efficient heuristics as well as two improved lower bounds that consistently outperform the existing methods. Additionally, we provide an effective Branch & Bound algorithm that can solve up to 100 jobs for some types of instances. These contributions not only enhance the theoretical comprehension of the problem but also offer efficient solutions supported by extensive statistical analysis over randomly generated instances.

Lattice is the main research subject in the geometry of numbers. SVP refers to finding a shortest nonzero lattice vector in a given lattice, which is thought to be a difficult optimization problem. For general lattice, the integer coefficients of a shortest nonzero vector under a lattice basis might be exponentially large, thus making the simple integer coefficient searching approach impractical. In this paper, we find that for low-dimensional circulant lattices(dimension (n in {2,3,4,6})), the integer coefficients of a shortest lattice vector under its circulant basis are actually in a small set (S={-1,0,1}), which makes it easy to find the shortest vector in these cases. Moreover, we present the specific forms of the SVP solutions for low-dimensional circulant lattices.

Gene trees inferred from molecular sequence alignments are typically unrooted, and determining the most credible rooting edge is a classical problem in computational biology. One approach to solve this problem is unrooted reconciliation, where the rooting edge is postulated based on the split of the root from a given species tree. In this paper, we propose a novel variant of the gene tree rooting problem, where the gene tree root is inferred using a phylogenetic network of the species present in the gene tree. To obtain the best rooting, unrooted reconciliation can be applied, where the unrooted gene tree is jointly reconciled with a set of splits inferred from the network. However, the exponential size of the set induced by display trees of the network makes this approach computationally prohibitive. To address this, we propose a broader and easier-to-control set of splits based on the structural properties of the network. We then derive exact mathematical formulas for the rooting problem and propose two general rooting algorithms to handle cases where the input network does not meet the initial requirements. Our experimental study based on simulated gene trees and networks demonstrates that our algorithms infer gene tree rootings correctly or with a small error in most cases.

Diabetes is regarded as one of the deadliest chronic illnesses that increases blood sugar. But there is no reliable method for predicting diabetic severity that shows how the disease will affect various body organs in the future. Therefore, this paper introduced Optimized Dual Directional Temporal convolution and Attention based Density Clustering (ODDTADC) method for predicting and classifying risk level in diabetic patients. In the diabetic prediction stage, the prediction is done by using an Integrated Dual Directional Temporal Convolution and an Enriched Remora Optimization Algorithm. Here, dual directional temporal convolution is used to extract temporal features by integrating dilated convolution and casual convolution in the feature extraction layer. Then, the attention module is used instead of max-pooling to emphasize the various features' importance in the feature aggregation layer. The Enriched Remora Optimization Algorithm is used to find optimal hyper parameters for Integrated Dual Directional Temporal Convolution. In the classification of stages based on risk level, the values from stage-I are fed into the Attention based Density Spatial Clustering of Applications with Noise, which allocate various weights based on their density values in the Core Points. Based on the results, the Nested Long Short-Term Memory is utilized to classify the risk levels of diabetic patients over a period of two or three years. Experimental evaluations were performed on five datasets, including PIMA Indian Diabetics Database, UCI Machine Learning Repository Diabetics Dataset, Heart Diseases Dataset, Chronic Disease Dataset and Diabetic Retinopathy Debrecen Dataset. The proposed ODDTADC method demonstrates superior performance compared to existing methods, achieving remarkable results in accuracy (98.21%), recall (94.46%), kappa coefficient (98.95%), precision (98.74%), F1-score (99.01%) and Matthew’s correlation coefficient (MCC) (0.87%).

The frustum model simulates network evolution by extending cliques, which represent highly interacting groups in social networks. In each time-step, new vertices are added adjacent to existing cliques of prescribed order. The model exhibits several features of social networks, such as densification, short distances, bad spectral expansion, and high local clustering.

The diameter of an undirected or a directed graph is defined to be the maximum shortest path distance over all pairs of vertices in the graph. Given an undirected graph G, we examine the problem of assigning directions to each edge of G such that the diameter of the resulting oriented graph is minimized. The minimum diameter over all strongly connected orientations is called the oriented diameter of G. The problem of determining the oriented diameter of a graph is known to be NP-hard, but the time-complexity question is open for planar graphs. In this paper we compute the exact value of the oriented diameter for triangular grid graphs. We then prove an n/3 lower bound and an (n/2+Oleft( sqrt{n}right) ) upper bound on the oriented diameter of planar triangulations, where n is the number of vertices in G. It is known that given a planar graph G with bounded treewidth and a fixed positive integer k, one can determine in linear time whether the oriented diameter of G is at most k. We consider a weighted version of the oriented diameter problem and show it to be weakly NP-complete for planar graphs with bounded pathwidth.

The problem studied in this paper is elective surgery scheduling, with resource constraints in each of the three following stages: preoperative, perioperative, and postoperative stages. With the integrated availability of hospital beds in wards and operating rooms, the aim is to determine operation start times of surgeries and allocate the hospital beds to patients while getting patients treated as soon as possible. This task is crucial in providing timely treatments for the patients while ensuring the hospital’s resource utilization balance. For the problem, we first formulate it as mixed-integer programming, which is NP-complete. Then, we propose several heuristics to overcome the long computation time. To make the solution better, we also propose improved algorithms. Finally, we conduct a series of numerical studies to illustrate the efficiency of our proposed algorithms and examine the impact of the number of jobs, beds, and surgery blocks on the performance measure. Computational experiments showed the superior performance of our heuristics in makespan.