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AbstractLet c: V(G) → {1, . . . , ℓ} = [ℓ] be a proper vertex coloring of G and C(i) = {u ∈ V(G): c(u) = i} for i ∈ [ℓ]. The k-color code rk(v|c) of vertex v is the ordered ℓ-tuple (aG(v,C(1)), . . . , aG(v,C(ℓ))) whereIf every two vertices have different color codes, then c is a (k, ℓ)-locating coloring of G. The k-locating chromatic number of graph G, denoted by , is the smallest integer ℓ such that G has a (k, ℓ)-locating coloring. In this paper, we propose this concept as an extension of diam(G)-locating chromatic number and 2-locating chromatic number which are known as the locating chromatic number, denoted χL(G), and neighbor-locating chromatic number, denoted , respectively. In this paper, we give sharp bounds for and where G◦H and are the corona and edge corona of G and H, respectively. We formulate an integer linear programming model to determine , noting that almost all graphs have diameter 2 and for every graph G of diameter 2. [ABSTRACT FROM AUTHOR]

A convex hull of finitely many points in the Euclidean space Rd is known as a convex polytope. Graphically, they are planar graphs i.e. embeddable on R2. Minimum dominating sets possess diverse applications in computer science and engineering. Locating-dominating sets are a natural extension of dominating sets. Studying minimizing locating-dominating sets of convex polytopes reveal interesting distance-dominating related topological properties of these geometrical planar graphs. In this paper, exact value of the locating-dominating number is shown for one infinite family of convex polytopes. Moreover, tight upper bounds on γl−d are shown for two more infinite families. Tightness in the upper bounds is shown by employing an updated integer linear programming (ILP) model for the locating-dominating number γl−d of a fixed graph. Results are explained with help of some examples. The second part of the paper solves an open problem in Khan (2023) [28] which asks to find a domination-related parameter which delivers a correlation coefficient of ρ>0.9967 with the total π-electronic energy of lower benzenoid hydrocarbons. We show that the locating-dominating number γl−d delivers such a strong prediction potential. The paper is concluded with putting forward some open problems in this area.

The optical network has become the most important way to carry power communications. To ensure its high reliability, operators need to detect the cables of the network periodically, which need to enter the substations. However, the large number and scattered location of substations bring challenges to the optical cable detection for the power communication optical network. This paper studies such multi-period optical cable detection problem of optical network in the context of power communication. With the objective of minimizing the total number of entered substations, we developed an Integer Linear Programming (ILP) model and a corresponding heuristic algorithm is also proposed. The simulation results show that the proposed heuristic algorithm can effectively reduce the total number of entered substations and perform close to the results of ILP model.

The optical network has become the most important way to carry power communications. To ensure its high reliability, operators need to detect the cables of the network periodically, which need to enter the substations. However, the large number and scattered location of substations bring challenges to the optical cable detection for the power communication optical network. This paper studies such multi-period optical cable detection problem of optical network in the context of power communication. With the objective of minimizing the total number of entered substations, we developed an Integer Linear Programming (ILP) model and a corresponding heuristic algorithm is also proposed. The simulation results show that the proposed heuristic algorithm can effectively reduce the total number of entered substations and perform close to the results of ILP model.

Space division multiplexing elastic optical networks (SDM-EONs) are one of the most promising network architectures that satisfy the rapidly growing traffic of the internet. However, different from traditional wavelength division multiplexing (WDM)-based networks, the problems of resource allocation become more complicated because SDM-EONs have smaller spectrum granularity and have to consider several novel network resources, such as modulation formats and spatial dimensions. In this work, we propose an integer linear programming (ILP) model without space lane change (SLC) that provides theoretically exact solutions for the problem of routing, modulation format, space, and spectrum assignment (RMSSA). Moreover, to more efficiently solve our model which is difficult to solve directly, we propose three exact algorithms based on model decomposition and evaluate their performance via simulation experiments, and we find that two of our exact algorithms can solve the model effectively in small-scale instances. [ABSTRACT FROM AUTHOR]

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Space division multiplexing elastic optical networks (SDM-EONs) are one of the most promising network architectures that satisfy the rapidly growing traffic of the internet. However, different from traditional wavelength division multiplexing (WDM)-based networks, the problems of resource allocation become more complicated because SDM-EONs have smaller spectrum granularity and have to consider several novel network resources, such as modulation formats and spatial dimensions. In this work, we propose an integer linear programming (ILP) model without space lane change (SLC) that provides theoretically exact solutions for the problem of routing, modulation format, space, and spectrum assignment (RMSSA). Moreover, to more efficiently solve our model which is difficult to solve directly, we propose three exact algorithms based on model decomposition and evaluate their performance via simulation experiments, and we find that two of our exact algorithms can solve the model effectively in small-scale instances.

A convex hull of finitely many points in the Euclidean space R d is known as a convex polytope. Graphically, they are planar graphs i.e. embeddable on R 2 . Minimum dominating sets possess diverse applications in computer science and engineering. Locating-dominating sets are a natural extension of dominating sets. Studying minimizing locating-dominating sets of convex polytopes reveal interesting distance-dominating related topological properties of these geometrical planar graphs. In this paper, exact value of the locating-dominating number is shown for one infinite family of convex polytopes. Moreover, tight upper bounds on γ l - d are shown for two more infinite families. Tightness in the upper bounds is shown by employing an updated integer linear programming (ILP) model for the locating-dominating number γ l - d of a fixed graph. Results are explained with help of some examples. The second part of the paper solves an open problem in Khan (2023) [28] which asks to find a domination-related parameter which delivers a correlation coefficient of ρ > 0.9967 with the total π -electronic energy of lower benzenoid hydrocarbons. We show that the locating-dominating number γ l - d delivers such a strong prediction potential. The paper is concluded with putting forward some open problems in this area., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2024 The Author(s).)

Abstract Background The haplotype assembly problem for diploid is to find a pair of haplotypes from a given set of aligned Single Nucleotide Polymorphism (SNP) fragments (reads). It has many applications in association studies, drug design, and genetic research. Since this problem is computationally hard, both heuristic and exact algorithms have been designed for it. Although exact algorithms are much slower, they are still of great interest because they usually output significantly better solutions than heuristic algorithms in terms of popular measures such as the Minimum Error Correction (MEC) score, the number of switch errors, and the QAN50 score. Exact algorithms are also valuable because they can be used to witness how good a heuristic algorithm is. The best known exact algorithm is based on integer linear programming (ILP) and it is known that ILP can also be used to improve the output quality of every heuristic algorithm with a little decline in speed. Therefore, faster ILP models for the problem are highly demanded. Results As in previous studies, we consider not only the general case of the problem but also its all-heterozygous case where we assume that if a column of the input read matrix contains at least one 0 and one 1, then it corresponds to a heterozygous SNP site. For both cases, we design new ILP models for the haplotype assembly problem which aim at minimizing the MEC score. The new models are theoretically better because they contain significantly fewer constraints. More importantly, our experimental results show that for both simulated and real datasets, the new model for the all-heterozygous (respectively, general) case can usually be solved via CPLEX (an ILP solver) at least 5 times (respectively, twice) faster than the previous bests. Indeed, the running time can sometimes be 41 times better. Conclusions This paper proposes a new ILP model for the haplotype assembly problem and its all-heterozygous case, respectively. Experiments with both real and simulated datasets show that the new models can be solved within much shorter time by CPLEX than the previous bests. We believe that the models can be used to improve heuristic algorithms as well.

Spin‐transfer torque random access memory (STT‐RAM) has emerged as an eminent choice for the larger on‐chip caches due to high density, low static power consumption and scalability. However, this technology suffers from long latency and high energy consumption during a write operation. Hybrid caches alleviate these problems by incorporating a write‐friendly memory technology such as static random access memory along with STT‐RAM technology. The proper allocation of data blocks has a significant effect on both performance and energy consumption in the hybrid cache. In this study, the allocation and migration problem of data blocks in the hybrid cache is examined and then modelled using integer linear programming (ILP) formulations. The authors propose an ILP model with three different objective functions which include minimising access latency, minimising energy and minimising energy‐delay product in the hybrid cache. Evaluations confirm that the proposed ILP model obtains better results in terms of energy consumption and performance compared to the existing hybrid cache architecture. [ABSTRACT FROM AUTHOR]

Elastic Optical Networks (EONs) using a flexible wavelength allocation technique with smaller granularity of spectrum can improve the efficiency and flexibility for diverse traffic transmission. However, due to the small granularity in EONs, the resource allocation problems become more complicated than that of the existing network architecture. By classifying the integer linear programming (ILP) models for solving the resource allocation problem on EONs into four categories, i.e., path/slot, path/channel, node/slot and node/channel, the characteristics of each are reviewed and tighter lower bounds estimation schemes for these ILP models are designed. Also, for channel models (i.e., path/channel and node/channel models), we propose two improved channel generation methods in pre-processing to reduce the number of variables. In the comparative experiments, we show the superiority of our methods, and by using them, analyze the characteristics of the four models. [ABSTRACT FROM AUTHOR]

Length-matching is an important technique to balance delays of bus signals in high-performance printed circuit board (PCB) routing. Existing routers, however, may generate very dense meander segments. Signals propagating along these meander segments exhibit a speedup effect due to crosstalk between the segments of the same wire, thus leading to mismatch of arrival times even under the same physical wire length. In this paper, we present a post-processing method to enlarge the width and the distance of meander segments and hence distribute them more evenly on the board so that crosstalk can be reduced. In the proposed framework, we model the sharing of available routing areas after removing dense meander segments from the initial routing, as well as the generation of relaxed meander segments and their groups for wire length compensation. This model is transformed into an ILP problem and solved for a balanced distribution of wire patterns. In addition, we adjust the locations of long wire segments according to wire priorities to swap free spaces toward critical wires that need much length compensation. To reduce the problem space of the ILP model, we also introduce a progressive fixing technique so that wire patterns are grown gradually from the edge of the routing toward the center area. Experimental results show that the proposed method can expand meander segments significantly even under very tight area constraints, so that the speedup effect can be alleviated effectively in high-performance PCB designs. [ABSTRACT FROM PUBLISHER]

This paper addresses the problem of spectrum-aware survivable strategies with failure probability constraints under static traffic in flexible bandwidth optical networks. The joint failure probability between primary and backup paths must be below the maximum tolerable joint failure probability for each traffic demand. We develop integer linear program (ILP) models for dedicated-path protection and shared-path protection in order to minimize the total number of frequency slots consumed, and we also propose a spectrum-aware dedicated protection (SADP) algorithm and a spectrum-aware shared protection (SASP) algorithm. Simulation results show that the ILP model solutions consume minimum number of frequency slots, but lead to higher average joint failure probability compared to the SADP and SASP algorithms. Moreover, both the SADP and SASP algorithms achieve a better performance in terms of total number of frequency slots consumed as compared to a conventional dedicated-path protection algorithm and a conventional shared-path protection algorithm, respectively, but lead to higher average joint failure probability. [ABSTRACT FROM PUBLISHER]

This paper considers the network protection technique of shared backup path protection (SBPP) in comparison with 1 + 1 path protection for elastic optical networks. We develop integer linear programming (ILP) models to minimize both the required spare capacity and the maximum number of link frequency slots (FSs) used. We consider transponder tunability that corresponds to the condition of whether or not the same set of FSs is required to be used for both the working and protection lightpaths. We also apply the bandwidth squeezed restoration technique to obtain the maximum restoration levels for the affected service flows, subject to a limited FS capacity on each fiber link. Our studies show that the proposed SBPP technique requires much lower spare capacity compared to the traditional 1 + 1 path protection approach. The flexibility of allowing the working and protection lightpaths to use different sets of FSs (i.e., with full transponder tunability) has the advantage of reducing both the number of FSs needed and the spare capacity redundancy required. [ABSTRACT FROM PUBLISHER]

Network Virtualization is claimed to be a key component of the Future Internet, providing the dynamic support of different networks with different paradigms and mechanisms in the same physical infrastructure. A major challenge in the dynamic provision of virtual networks is the efficient embedding of virtual resources into physical ones. Since this problem is known to be NP-hard, previous research focused on designing heuristic-based algorithms; most of them either do not consider a simultaneous embedding of virtual nodes and virtual links, or apply link-path formulation, leading to non-optimal solutions. This paper proposes an integer linear programming (ILP) formulation to solve the online virtual network embedding problem as a result of an objective function striving for the minimization of resource consumption and load balancing. To this end 3 different objective functions are proposed and evaluated. This approach applies multi-commodity flow constraint to accomplish a node-link formulation that optimizes the allocation of physical network resources. This proposal is evaluated against state of the art heuristics. The performance of the heuristics related to Virtual Network (VN) request acceptance ratio is, at least, 30% below the one of the Virtual Network Embedding Node-Link Formulation (VNE-NLF) method. From the three cost functions evaluated, the Weighted Shortest Distance Path (WSDP) is the one which embeds more VNs and also requires, on average, less physical resources per embedding. [ABSTRACT FROM PUBLISHER]

Countries around the world have tightened their border controls in response to the spread of COVID-19. Consequently, seafarers are prohibited from boarding or leaving ships at most ports, with few exceptions. This situation means that seafarers are highly likely to serve onboard vessels beyond their contracted shifts. Most seafarers are prone to depression because they have to spend long periods at sea away from family and friends, and, thus, banning crew changes will put their mental health further at risk. This will increase the likelihood of maritime accidents, thus jeopardizing global supply chains and ultimately exacerbating current hardships. To tackle this emergency, the International Maritime Organization and the European Commission have called on governments to coordinate efforts to designate ports for crew changes during the pandemic. This study aims to solve the crew change problem by using an integer linear programming model. In the sensitivity analysis section, we find that the number of opening ports for crew changes and the cost of crew changes decrease when the cost of opening ports increases. The results show governments will not invest in opening more ports when the cost of opening ports increases. However, the penalty increases when the number of open ports decreases, and the cost of opening ports increases. As the number of crew changes is decreasing, this leads to the penalty increasing, when the number of open ports decreases. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the problem of survivable routing of static demands in connection-oriented WDM networks with shared protection. We first discuss conditions and characteristics of a typical backup path sharing approach with respect to the average length of backup paths, and the values of connection restoration time. Next we propose a new method of sharing the backup paths, called SPGC, which is the first one that does not increase the length of backup paths (thus providing fast restoration of broken connections). The respective ILP model has been introduced. Owing to the complexity of the SPGC problem, an efficient heuristic algorithm designed for the general case of limited wavelength conversion capability has been also proposed. Extensive numerical experiments have shown that the proposed backup path sharing approach provides values of service recovery time which are up to 50% shorter on average, compared to the typical sharing technique. These results were achieved together with a significant reduction of the total link capacity utilization ratio of up to 40%. [ABSTRACT FROM PUBLISHER]

This study considers the scheduling problem observed in the burn-in operation of semiconductor final testing, where jobs are associated with release times, due dates, processing times, sizes, and non-agreeable release times and due dates. The burn-in oven is modeled as a batch-processing machine which can process a batch of several jobs as long as the total sizes of the jobs do not exceed the machine capacity and the processing time of a batch is equal to the longest time among all the jobs in the batch. Due to the importance of on-time delivery in semiconductor manufacturing, the objective measure of this problem is to minimize total weighted tardiness. We have formulated the scheduling problem into an integer linear programming model and empirically show its computational intractability. Due to the computational intractability, we propose a few simple greedy heuristic algorithms and meta-heuristic algorithm, simulated annealing (SA). A series of computational experiments are conducted to evaluate the performance of the proposed heuristic algorithms in comparison with exact solution on various small-size problem instances and in comparison with estimated optimal solution on various real-life large size problem instances. The computational results show that the SA algorithm, with initial solution obtained using our own proposed greedy heuristic algorithm, consistently finds a robust solution in a reasonable amount of computation time. [ABSTRACT FROM AUTHOR]

Abstract: We have examined InAs-based heterostructure whose Rashba effect is made anomalously large by band-gap engineering. Shubnikov–de Haas oscillation and weak antilocalization (WAL) were measured under positive and negative gate voltages, respectively, to examine the gate modulation of Rashba effect in the InAs-based heterostructure. Suppression of WL in positive and slightly negative gate voltage region (V g >−0.3V) is presumably caused by the increased Rashba effect due to band discontinuity under the peak position of wavefunction. WL appearance in the middle range of gate voltage bias was explained consistently with the decreased SO effect in the gate voltage region where sign change of Rashba factor takes place. [Copyright &y& Elsevier]

• A new methodology to assist a forecaster to select the appropriate technique using fuzzy sets. • Suitable criteria for selecting a technological forecasting technique. • A challenging case from the aviation technologies with the existence of uncertainty and ambiguity. The technology changes and developments in the world are very rapid and has led many countries and organizations to try to keep up with them through acquisition of technology. Choosing the right method as one of the steps in the technology transfer (TT) process has a significant impact on the successful implementation of technology acquisition (TA). The purpose of this study is to select the most appropriate method of acquiring interactive TV technology for MTN Irancell Telecommunication Company using a combined model of multi-criteria decision-making (MCDM) methods. Therefore, in this research, in the first stage of structuring, the list of criteria and alternatives was determined based on a literature review. Then, in the assessment phase, the fuzzy Delphi technique was used to finalize the list of criteria and alternatives, and then an improved fuzzy group hierarchical best-worst method (fuzzy G-HBWM) was used to determine the criteria weights and evaluate the alternatives by an expert group to form a decision matrix. Finally, in the ranking stage, the alternatives were ranked using fuzzy multi-attribute decision-making (F-MADM) methods including ARAS-F, fuzzy TOPSIS, fuzzy WASPAS, fuzzy VIKOR, fuzzy MABAC, and fuzzy SAW. Then, the Integer Linear Program (ILP) model was used to aggregate the ranking. Based on the results, the main criteria in order of importance are: technology factors, environmental and market factors, organizational factors, and partner or vendor factors. Also, the most important sub-criteria can be considered, respectively, as: the innovative rate in the industry, the degree of strategic importance of technology, the need for access to technology, and the ability to share assets. The final ranking results showed that turnkey contracts, stock ownership, and outsourcing are the top three alternatives in order of priority. [ABSTRACT FROM AUTHOR]