Journal of Combinatorial Optimization最新文献

There are numerous combinatorial algorithms for classical min-cost flow problems and their simpler variants like max flow or shortest path problems. It is well-known that many of these algorithms are related to the Simplex method and the more general circuit augmentation schemes: prime examples are the network Simplex method, a refinement of the primal Simplex method, and min-mean cycle canceling, which corresponds to a steepest-descent circuit augmentation scheme. We are interested in a deeper understanding of the relationship between circuit augmentation and combinatorial network flows algorithms. To this end, we generalize from primal flows to so-called pseudoflows, which adhere to arc capacities but allow for a violation of flow balance. We introduce ‘pseudoflow polyhedra,’ wherein slack variables are used to quantify this violation, and characterize their circuits. This enables the study of combinatorial network flows algorithms in view of the walks they trace in these polyhedra, and the pivot rules for the steps. In doing so, we provide an ‘umbrella,’ a general framework, that captures several algorithms. We show that the Successive Shortest Path Algorithm for min-cost flow problems, the Shortest Augmenting Path Algorithm for max flow problems, and the Preflow-Push algorithm for max flow problems lead to (non-edge) circuit walks in these polyhedra. The former two are replicated by circuit augmentation schemes for simple pivot rules. Further, we show that the Hungarian Method leads to an edge walk and is replicated, equivalently, as a circuit augmentation scheme or a primal Simplex run for a simple pivot rule.

In this paper, we study the independent quadratic assignment problem which is a variation of the well-known Koopmans–Beckman quadratic assignment problem. The problem is strongly NP-hard and is also hard to approximate. Some polynomially solvable special cases are identified along with a complete characterization of linearizable instances of the problem, the validity of which is shown to be verifiable in linear time. This improves the existing quadratic bound for this problem. Additional complexity results are also presented.

Substar reliability defined as the probability that a fault-free substar of a certain scale is still available in the star network (S_n) when the occurrence of faults. The substar reliability is one of the most practical reliability measures because a user in the current star multiprocessors is given a certain substar for the execution of his/her program. Wu and Latifi(Inf. Sci. 178 (2008)) derived upper-bound on the substar reliability of (S_n) by analysing the intersection of no more than three substars. Later, Li et al.(IEEE. Trans. Rel. 65 (2016)) derived lower-bound on the substar reliability of (S_n) by considering the intersection of no more than four substars. In the paper, we further derive the upper- and lower bounds on the substar reliability of (S_n) by taking into account the intersection of no more than five or four substars, respectively. At a result, we obtain more accurate value of the upper-bound on substar reliability of (S_n). The experimental study indicates that both the upper- and lower bounds are very close to approximate results especially for the low value of the node reliability.

We study the SONET edge partition problem that models telecommunication network design to partition the edge set of a given graph into several edge-disjoint subgraphs, such that each subgraph has size no greater than a given capacity k and the sum of the orders of these subgraphs is minimized. The problem is NP-hard when (k ge 3) and admits an (O(log k))-approximation algorithm. For small capacity (k = 3, 4, 5), by observing that some subgraph structures are more favorable than the others, we propose modifications to existing algorithms and design novel amortization schemes to prove their improved performance. Our algorithmic results include a (frac{4}{3})-approximation for (k = 3), improving the previous best (frac{13}{9})-approximation, a (frac{4}{3})-approximation for (k = 4), improving the previous best ((frac{4}{3} + epsilon ))-approximation, and a (frac{3}{2})-approximation for (k = 5), improving the previous best (frac{5}{3})-approximation. Besides these improved algorithms, our main contribution is the amortization scheme design, which can be helpful for similar algorithms and problems.

L-shaped floorplans are defined by rectangular modules enclosed within a rectilinear outer boundary, forming an L-shape that can not be altered through simple extension or contraction of a boundary wall. The boundary of such floorplans comprises five convex corners and one concave corner. The concave corner on the boundary of the plan can not be converted into a convex corner without altering the horizontal and vertical adjacency among the modules. This paper introduces a linear-time algorithm based on canonical ordering to generate L-shaped floorplans from properly triangulated plane graphs (PTPGs). Here, modules in the floorplan correspond to the nodes of the given graph, while edges in the graph represent wall adjacency between modules. The proposed algorithm assigns a unique labeling to the given graph, ensuring the presence of a concave corner on the resulting floorplan’s boundary. Simple boundary wall extensions or contractions cannot eliminate this concave corner. It also produces multiple L-shaped floorplans corresponding to the given PTPG, with variations mainly on their concave corners, highlighting the unique configurations possible within the same boundary constraints. Our algorithm offers simplicity over existing methods and is easy to implement. Additionally, we have implemented the algorithm in Python, enabling easy integration for generating L-shaped floorplans in various architectural and VLSI circuit design applications.

Diagnosis of thyroid disease is a most important cause in the field of medicinal research and it is a complex onset axiom. Secretion of Thyroid hormone plays a major role in the regulation of metabolism. Hence, it is very significant to predict thyroid disease in the initial stage, which is helpful for preventing more serious health complications due to thyroid cancer. The diagnostic accuracy of machine leaning-based approaches is greater but these techniques require large amounts of data for the diagnosis process. In the conventional approaches, the time needed for the prediction process is also high. Feature engineering is less investigated in conventional models and hence error produced during the prediction process is high. Hence, in this research work, a machine learning-aided thyroid disease prediction technique is designed to provide higher prediction accuracy and reliability. Initially, the thyroid data is gathered from the standard benchmark resources. Next, the data transformation process is carried out to make the data usable for analysis and visualization. After, the features are extracted using Principal Component Analysis (PCA), “One-Dimensional Convolutional Neural Network Model (1DCNN). Moreover, the statistical features are also extracted for getting more relevant information from the data. The three sets of features such as PCA-based, 1DCNN-based and statistical are concatenated and fed to the “optimal weighted feature selection” process, where the optimal features and weights are tuned by an Improved Archimedes Optimization Algorithm (IAOA). Next, the selected optimally fused features are given to the Ensemble Learning (EL) for predicting the thyroid diseases, where the EL with be suggested by incorporating stacking classifier, XGboost, and Multivariate regression classifier. Ensembling of three different classifiers provides higher thyroid disease prediction accuracy and it makes the decision about normal and abnormal classes. Here, the same IAOA is used for optimizing the parameters of every classifier. The investigational outcomes demonstrate that the proposed ensemble classifier provides higher performance than others. Experimental results prove that the thyroid prediction accuracy of the developed EL approach is 96.30%, precision is 99.67% and F1-score is 97.93%, which is more extensive than the state-of-the-art approaches.

In a graph G, the normal k-edge coloring (sigma ) is defined as the conventional edge coloring of G using the color set (left[ k right] =left{ 1,2,cdots ,k right} ). If the condition (Sleft( u right) ne Sleft( v right) ) holds for any edge (uvin Eleft( G right) ), where (Sleft( u right) =sum nolimits _{uvin Eleft( G right) }{sigma left( uv right) }), then (sigma ) is termed a neighbor sum distinguishable k-edge coloring of the graph G, abbreviated as k-VSDEC. The minimum number of colors ( k ) needed for this type of coloring is referred to as the neighbor sum distinguishable edge chromatic number of ( G ), represented as ( chi '_{varSigma }(G) ). This paper examines neighbor sum distinguishable k-edge colorings in the joint graphs of an h-order path ({{P}_{h}}) and an (left( z+1 right) )-order star ({{S}_{z}}), providing exact values for their neighboring and distinguishable edge coloring numbers, which are either (varDelta ) or (varDelta +1).

In recent years, k-submodular functions have garnered significant attention due to their natural extension of submodular functions and their practical applications, such as influence maximization and sensor placement. Influence maximization involves selecting a set of nodes in a network to maximize the spread of information, while sensor placement focuses on optimizing the locations of sensors to maximize coverage or detection efficiency. This paper first proposes two randomized algorithms aimed at improving the approximation ratio for maximizing monotone k-submodular functions under matroid constraints and individual size constraints. Under the matroid constraints, we design a randomized algorithm with an approximation ratio of (frac{nk}{2nk-1}) and a complexity of (O(rn(text {RO}+ktext {EO}))), where n represents the total number of elements in the ground set, k represents the number of disjoint sets in a k-submodular function, r denotes the size of the largest independent set, (text {RO}) indicates the time required for the matroid’s independence oracle, and (text {EO}) denotes the time required for the evaluation oracle of the k-submodular function.Meanwhile, under the individual size constraints, we achieve an approximation factor of (frac{nk}{3nk-2}) with a complexity of O(knB), where n is the total count of elements in the ground set, and B is the upper bound on the total size of the k disjoint subsets, belonging to (mathbb {Z_{+}}). Additionally, this paper designs two double randomized algorithms to accelerate the algorithm’s running speed while maintaining the same approximation ratio, with success probabilities of ((1-delta )), where (delta ) is a positive parameter input by the algorithms. Under the matroid constraint, the complexity is reduced to (O(nlog rlog frac{r}{delta }(text {RO}+ktext {EO}))). Under the individual size constraint, the complexity becomes (O(k^{2}nlog frac{B}{k}log frac{B}{delta })).

Today, artificial bee colony (ABC) algorithm is one of the most popular swarm intelligence based optimization techniques. Although it was originally introduced to work on continuous space for numerical optimization problems, several researchers also successfully use the ABC for other problem types. In this study, variants of the ABC for scheduling problems are surveyed. Since the scheduling problems are combinatorial type problems, generally some modifications related to the solution representation or neighborhood search operators are introduced in these studies. Additionally, several enhancement ideas are also presented for the ABC algorithm such as the improvements of initialization, employed bee, onlooker bee, scout bee phases and hybrid usage with other metaheuristics or local search methods. This paper evaluates the literature, provides some analyses on its current state and gaps, and addresses possible future works. It is hoped that this review study would be beneficial for the researchers interested in this field.

In the A-Multi3-Hitting Set problem (A-M3HS), where (A subseteq {1,2,3}), the input is a hypergraph G in which the hyperedges have sizes at most 3 and an integer k, and the goal is to decide if there is a set S of at most k vertices such that (|S cap e| in A) for every hyperedge e. In this paper we give (O^*(2.027^k))-time algorithms for ({1})-M3HS and ({1,3})-M3HS, and an (O^*(1.381^k))-time algorithm for ({2})-M3HS.