The study of heterogeneous clusters or networks of work- stations has received a good deal attention , , , . The scheduling of tasks with precedence constraints, which are usually represented by Directed Acyclic Graphs (DAG), has also been well documented , , , , , , . An off-line algorithm is presented in  to schedule commu- nicating tasks with precedence constraints in distributed sys- tems. However, the algorithm belongs to the static category. In  a dynamic incremental DAGscheduling approach for parallel machines is described. However, the approach is lim- ited to homogenous systems. Two low-complexity efficient heuristics, the Heterogeneous Earliest-Finish-Time Algorithm and the Critical-Path-on-a-Processor Algorithm are proposed in , each for the scheduling of DAGs on heterogeneous processors. These heuristics are not designed for real-time task allocation and are therefore not suitable for scheduling in a real-time context because job requirements cannot be guaran- teed. In  non-real-time DAGs are extended to include real-time information, and the scheduling of parallel tasks with real-time DAG topologies on heterogeneous systems is pro- posed. This technique differs from that presented in this paper because it is not aimed at the utilization of spare system capa- bilities.
Scheduling of any of the above kind is called as DAGscheduling which aims (i) to reduce the schedule length (makespan), (ii) to improve the scheduling efficiency by minimizing communication delay, (iii) to effectively balance the load among the resources. Task scheduling problem is an application that could be shown through a DAG. DAG can be expressed as G= (T, E), where, ‘G’ is the directed acyclic graph,
Over the past few decades, research efforts are mainly focused on the problem of task scheduling on algorithms running on homogenous and heterogeneous systems mainly with the objective of reducing the overall execution time of the tasks. Topcuoglu et al.  have presented HEFT and CPOP scheduling algorithms for heterogonous processors. Luiz et al.  have developed lookahead-HEFT algorithm, which look ahead in the schedule to make scheduling decisions. Eswari, R. and Nickolas, S.  have proposed PHTS algorithm to efficiently schedule tasks on the heterogeneous distributed computing systems. Rajak and Ranjit  have presented a queue based scheduling algorithm called TSB to schedule tasks on homogeneous parallel multiprocessor system. Ahmed, S.G.; Munir, E.U.; and Nisar, W.  have developed genetic algorithm called PEGA that provide low time complexity than standard genetic algorithm (SGA). Xiaoyong Tang; Kenli Li; Renfa Li; and Guiping Liao  have presented a list- scheduling algorithm called HEFD for heterogeneous computing systems. Nasri, W. and Nafti, W.  have developed a new DAGscheduling algorithm for heterogeneous systems that provide better performance than some well-known existing scheduling algorithms.
SimJava framework is used for core simulation facilities. For modeling Grid resources, Grid Information Service, and Grid tasks, GridSim toolkit is used. The Application Scheduler is in Application Broker layer. This Application Scheduler carries out activities that are involved in scheduling tasks of a DAG application. The DAG Application Scheduler GUI, which works as Grid Application layer, has three GUI consoles: DAG GUI, Resource GUI, and Schedule GUI. The DAG GUI is responsible for creating a DAG application by performing drag and drop of tasks and links. The Resource GUI is responsible for taking Grid resource information from the user. The Scheduler GUI is responsible for displaying the assignment of tasks of DAG on the selected resources. The decision regarding which task should be assigned to which resource is taken by the Application Scheduler. The researcher who wants to use this proposed DAGscheduling simulator can change the scheduling algorithm in this Application Scheduler component for study and research.
The HEFT Algorithm is one of the best and well accepted list deployed heuristics. The HEFT calculation is a compelling answer for the DAGScheduling issue on heterogeneous framework. The confinement of HEFT calculation is that it utilizes procedures that are all static methodologies of the mapping issue that accept static conditions for a given time. HEFT is a two- phase scheduling algorithm with the heterogeneous processors. The phase which is used to assign the priority to tasks is the first phase, known as the task prioritization phase and for assigning the priority, the upward rank of every task is calculated. The upward rank is the critical path of the task that is the maximum amount of communication time and the average implementation time right from the start of any task to the end of any task. The phase which is used to schedule the tasks into the process which provides the EFT of the task is the Processor Selection phase (second phase). This phase has the insertion based
To illustrate, a small scale DAGscheduling problem involving 3 nodes and 10 tasks is considered (Fig 2) with the computation cost matrix given in Table 1.The upward rank and the order of the tasks for execution are given in Table 2 and 3 respectively. RASA algorithm was executed with the following parameters. Size of the population -15, T_frac -10 -2 , T_frac_min - 10 -4 , T_mult -0.9, Parameter q -0.09, Scaling factor -0.8, successmax(SM)- 2,Number of iterations- 50. The makespan value obtained for the example problem is found to be 73.
Although one automaton can define both single- and multi-rooted DAG languages, these languages are incomparable. Drewes (2017) uses a construc- tion very similar to the one in Theorem 1 to show that single-rooted languages have very expressive path languages, which he argues are too expressive for modeling semantics. 5 Since the constructions are so similar, it natural to wonder if the problem that single-rooted automata have with probabili- ties is related to their problem with expressivity, and whether it likewise disappears when we allow multiple roots. We now show that multi-rooted languages have the same problem with probabil- ity, because any multi-rooted language contains the single-rooted language as a sublanguage. Corollary 1. Let A be the automaton defined in Example 1. There is no w that makes (A, w) prob- abilistic with full support over L m (A).
Dag Hammarskjold (1905-1961), of Sweden, was elected Secretary-General of the United Nations by the General assembly on 7 April 1953, taking the oath of office on 10 April 1953. He was re-elected for a second 5-year term in September 1957. On 18 September 1961 Secretary-General Hammarskjold was killed in an airplane accident during a tour in Congo.
The VLab science gateway is based around the JSR 168  portlet model, and the initial set of VLab portlets are described in detail in . We began by developing Grid portlets using the OGCE  software. In this model, each portlet application was responsible for an individual task. For example, one portlet is getting Grid credentials from MyProxy  repository, another one is for GridFTP file operation. A third portlet is used to execute Quantum Espresso  package, which is major high performance computing application for VLab material science research. This approach is useful for general user portals but needs to be modified for application-specific portals like VLab. That is, we need to collect multiple capabilities within science application- specific portlets and to handle complicated Quantum Espresso job executions and file transfers in a sequence; that is, we must define dependencies between atomic job tasks. Consequently, we have determined that we can represent job dependencies using Directed Acyclic Graphs (DAG) .
On the basis of these observations, the following joint strategies can be adopted to reduce the storage requirements: i) the input tree is read using a depth-first visit and as soon as a vertex completes the computation of its C(u, v) entries, the storage space for the C(u, v) entries referring to its children is deallocated; ii) for each distinct production, a list of matching vertices in the DAG is maintained with the aim of both speeding up the search for a production match, and also to assign a progressive numerical id to the matching vertices as well as the total number of matching vertices to the production; in this way, when a new vertex in the input tree is visited, it is possible to know how much storage space must be dynamically allocated for that vertex. It should be noticed that each list associated with a production can be maintained very efficiently by just: (1) using a counter c recording the current total number of vertices belonging to the list; (2) assigning as id to a new vertex the current value of c; (3) inserting the new vertex at the beginning of each list and incrementing c by 1. All the above operations can be done in constant time. The application of the above strategies reduces the storage need from O(N dag N tree ), where N dag is the number of nodes in the DAG, and N tree is the
The VLab science gateway is based around the JSR 168 portlet model, and the initial set of VLab portlets are described in detail in . We began by developing Grid portlets using the OGCE  software. In this model, each portlet application was responsible for an individual task. For example, one portlet retrieves Grid credentials from a MyProxy repository, another one is for GridFTP file operation, and a third portlet is used to execute Quantum Espresso  package, which is major high performance computing application for VLab material science research. This approach is useful for general user portals but needs to be modified for application-specific portals like VLab. We need to collect multiple capabilities within a single science application- specific portlet and handle complicated Quantum Espresso job executions and file transfers in a sequence. We must define dependencies between atomic job tasks. Consequently, we have determined that we can represent job dependencies using Directed Acyclic Graphs (DAG) .
If we look at the tasks of a supply chain we find different areas where scheduling problems have to be solved. Starting with the final products to be delivered there has to be a master schedule which says how much of these products should be available at what times. From that we can schedule when products have to be assembled, when parts have to be produced, stored and transported, and what raw materials have to be purchased. This is more or less a global scheduling task where a schedule for all the participating partners of the supply chain has to be generated. This global schedule can be separated into several schedules for the companies involved, e.g., a global production schedule, a global transportation schedule, etc. This is what APS (advanced planning and scheduling) systems are doing thereby using predictive scheduling approaches [3; 13]. But this is only a part of the solution of the supply chain scheduling problem because the global schedules have to be put into action within the companies which means that the companies too, have to create schedules for the tasks within their business units. And these business units have to create schedules for resource groups or for single resources. Thus we have a lot of interrelated scheduling problems on different organizational levels with schedules for each of the business units or resources. And what if the schedule on a lower level is disrupted and reactive scheduling has to be performed for the business unit involved. If the changed schedule will not affect the global schedule, this will be fine. But if the global schedule is affected too, which means that preceding or following activities cannot be performed as previously scheduled, then those have to be rescheduled too. This can lead to a rescheduling task even for the top level global schedules. This also means that schedule revision is a continuous process. So we are faced with predictive as well as reactive scheduling tasks on all levels. Additionally, we have to consider: • interdependencies between production processes that are performed in different
Operation scheduling minimize the throughput times of material and capital commitment and to ensure that capacities are fully utilized and that operating resources and labour cost are kept low in order to increase the performance of the firm (Schuh, 2006). Also, the operation schedule helps to improve productivity and minimizes the makespan (the total amount of time required to complete a group of jobs) and product delivery time. Production Managers are mainly concerned with the short-term tasks such as scheduling, maintaining efficiency levels, monitoring controls and resolving factory labour problems. However, the concept of managing production has moved to the complexity in product range, product mix, volume changes, process flexibility, inventory, cost and financial controls, and employee awareness because of the more intensive level of domestic and international competition (Hill, 2000).
Note that the nodes of the DAG are all en- closed in a higher-level node situated on Satur- day. This ‘envelope’ provides the framework for the detailed events. However, within this enve- lope, a branching occurs, separating Watson’s ex- plicitly noted activities from those which we must suppose Holmes to have accomplished. The two series are bracketed between a relative temporal marker (the moment when Watson and Holmes leave each other) and an absolute temporal marker (Watson’s arrival at Holmes’ lodgings around 10). 4.3 Access to Encyclopaedic Information Reading a text is not a simple activity. Among other things, it requires a constant reference to background ‘encyclopaedic’ information. The na- ture of this information will vary from reader to reader. As an illustration, consider the fol- lowing paragraph, which opens Flaubert’s novel Salammbˆo. 11
Consideration of the entire GH threading shows not just return of the thread to a single node, but also con- stellations of nodes which ‘hang together’. In some cases, this is based on common membership of the nodes in some class of events. One example of this is provided by Phil’s various attempts at suicide. Since Phil returns to life after each suicide, each suicide attempt (a toaster dropped into a bathtub, leaping from a tall building, walking in front of a bus, and so on) shares with the others only membership in the class of suicide events. This state of affairs may be captured by including each of these nodes within a local subDAG, which itself represents a subnode of the larger DAG. So, for example, we could represent the local subDAG here by means of the semantic expression attempt(phil, suicide). Such subDAGs may be further refined or combined, sim- ilar to the concept of stepwise refinement found in computer programming.
However, successfully building large scale knowledge bases with maximum coverage is not possible by a single person or a small group of people without collaborative support. In this paper, we have presented our approach on information visualization and management of linguistic and concepts/ontologies. In our visualization method we represent ontology as a directed acyclic graph (DAG) . Providing a visual hierarchy is one of the main goals in structuring information presentations. Presenting data as in graph is one way of structuring information. However it is well known that understanding and comprehensive analysis of data in graph structures is easiest if the size of the presented graph is small. Therefore we employ an incremental browsing method of the information space structure and visualizes in every moment only specific part of the information where its content depend on previous action.
In the first step, the process of detection and classification of the desired tool is carried out, where all objects are extracted from the work environment, covered with a detection box and classified with the DAG- CNN, to determine if the scalpel is occluded or not. In the second step, the manipulator is moved to each of the occlusions and removed them, one by one, until free the scalpel, which is grabbed and left in the center of the table. The program ends only when all occlusions have been removed and the scalpel has been ordered.