如何使用 LINQ to Objects 安排作业而不重叠？

Question

这是另一个资源分配问题。我的目标是运行一个查询，将任何时隙的最高优先级作业分配给两个 CPU 核心之一（只是一个示例，所以我们假设没有中断或多任务处理）。注意：这类似于我之前关于分区的文章，但重点关注重叠时间和分配多个项目，而不仅仅是最优先的项目。

这是我们的目标：

public class Job
{
    public int Id;
    public int Priority;
    public DateTime Begin;
    public DateTime End;
}

真实的数据集非常大，但对于这个例子，假设有 1000 个作业分配给两个 CPU 核心。它们都加载到内存中，我需要对它们运行单个 LINQ to Objects 查询。目前，这需要近 8 秒和 140 万次比较。

我利用了这篇文章中引用的逻辑确定两个项目是否重叠，但与该帖子不同的是，我不需要简单地找到重叠的项目，而是需要安排任何重叠集的顶部项目，然后安排下一个项目。

在讨论代码之前，让我指出当前无效算法的步骤：

1. 确定剩余的作业（通过删除任何已分配的作业）
2. 通过自连接所有剩余作业并按优先级选择顶部重叠作业，将作业分配给当前核心。
3. 通过执行查询连接新作业
4. 对每个剩余核心从停止 1 开始重复

问题：

• 如何才能最有效地做到这一点？
• 我可以避免步骤2中的子查询吗？也许通过分组，但我不确定如何根据 .Overlaps() 扩展方法进行分组。
• 这些工作已经被订购。第 2 步是否可以利用这一事实，只与短范围内的项目进行比较，而不是与每个作业进行比较？
• 有没有比循环更有效的分配给核心的方法？这样可以避免执行第3步中的查询吗？同样，如果我可以对重叠作业集进行分组，那么分配核心只需为每个重叠作业集选择 N 个即可。

完整示例代码：

public class Job
{
    public static long Iterations;

    public int Id;
    public int Priority;
    public DateTime Begin;
    public DateTime End;

    public bool Overlaps(Job other)
    {
        Iterations++;
        return this.End > other.Begin && this.Begin < other.End;
    }
}

public class Assignment
{
    public Job Job;
    public int Core;
}

class Program
{
    static void Main(string[] args)
    {
        const int Jobs = 1000;
        const int Cores = 2;
        const int ConcurrentJobs = Cores + 1;
        const int Priorities = Cores + 3;
        DateTime startTime = new DateTime(2011, 3, 1, 0, 0, 0, 0);
        Console.WriteLine(string.Format("{0} Jobs x {1} Cores", Jobs, Cores));
        var timer = Stopwatch.StartNew();

        Console.WriteLine("Populating data");
        var jobs = new List<Job>();
        for (int jobId = 0; jobId < Jobs; jobId++)
        {
            var jobStart = startTime.AddHours(jobId / ConcurrentJobs).AddMinutes(jobId % ConcurrentJobs);
            jobs.Add(new Job() { Id = jobId, Priority = jobId % Priorities, Begin = jobStart, End = jobStart.AddHours(0.5) });
        }
        Console.WriteLine(string.Format("Completed in {0:n}ms", timer.ElapsedMilliseconds));
        timer.Restart();

        Console.WriteLine("Assigning Jobs to Cores");
        IEnumerable<Assignment> assignments = null;
        for (int core = 0; core < Cores; core++)
        {
            // avoid modified closures by creating local variables
            int localCore = core;
            var localAssignments = assignments;

            // Step 1: Determine the remaining jobs
            var remainingJobs = localAssignments == null ? 
                                                jobs :
                                                from j in jobs where !(from a in localAssignments select a.Job).Contains(j) select j;

            // Step 2: Assign the top priority job in any time-slot to the core
            var assignmentsForCore = from s1 in remainingJobs
                              where
                                  (from s2 in remainingJobs
                                   where s1.Overlaps(s2)
                                   orderby s2.Priority
                                   select s2).First().Equals(s1)
                              select new Assignment { Job = s1, Core = localCore };

            // Step 3: Accumulate the results (unfortunately requires a .ToList() to avoid massive over-joins)
            assignments = assignments == null ? assignmentsForCore.ToList() : assignments.Concat(assignmentsForCore.ToList());
        }

        // This is where I'd like to Execute the query one single time across all cores, but have to do intermediate steps to avoid massive-over-joins
        assignments = assignments.ToList();

        Console.WriteLine(string.Format("Completed in {0:n}ms", timer.ElapsedMilliseconds));
        Console.WriteLine("\nJobs:");
        foreach (var job in jobs.Take(20))
        {
            Console.WriteLine(string.Format("{0}-{1} Id {2} P{3}", job.Begin, job.End, job.Id, job.Priority));
        }

        Console.WriteLine("\nAssignments:");
        foreach (var assignment in assignments.OrderBy(a => a.Job.Begin).Take(10))
        {
            Console.WriteLine(string.Format("{0}-{1} Id {2} P{3} C{4}", assignment.Job.Begin, assignment.Job.End, assignment.Job.Id, assignment.Job.Priority, assignment.Core));
        }

        Console.WriteLine(string.Format("\nTotal Comparisons: {0:n}", Job.Iterations));

        Console.WriteLine("Any key to continue");
        Console.ReadKey();
    }
}

示例输出：

1000 个作业 x 2 个核心
填充数据
0.00ms 内完成
将作业分配给核心
在 7,998.00 毫秒内完成

职位：
3/1/2011 12:00:00 AM-3/1/2011 12:30:00 AM Id 0 P0
3/1/2011 12:01:00 AM-3/1/2011 12:31:00 AM Id 1 P1
3/1/2011 12:02:00 AM-3/1/2011 12:32:00 AM Id 2 P2
3/1/2011 1:00:00 AM-3/1/2011 1:30:00 AM Id 3 P3
3/1/2011 1:01:00 AM-3/1/2011 1:31:00 AM Id 4 P4
3/1/2011 1:02:00 AM-3/1/2011 1:32:00 AM Id 5 P0
3/1/2011 2:00:00 AM-3/1/2011 2:30:00 AM Id 6 P1
3/1/2011 2:01:00 AM-3/1/2011 2:31:00 AM Id 7 P2
3/1/2011 2:02:00 AM-3/1/2011 2:32:00 AM Id 8 P3
3/1/2011 3:00:00 AM-3/1/2011 3:30:00 AM Id 9 P4
2011 年 3 月 1 日 3:01:00 AM-2011 年 3 月 1 日 3:31:00 AM Id 10 P0
3/1/2011 3:02:00 AM-3/1/2011 3:32:00 AM Id 11 P1
3/1/2011 4:00:00 AM-3/1/2011 4:30:00 AM Id 12 P2
3/1/2011 4:01:00 AM-3/1/2011 4:31:00 AM Id 13 P3
3/1/2011 4:02:00 AM-3/1/2011 4:32:00 AM Id 14 P4
2011/3/1 5:00:00 AM-2011/3/1 5:30:00 AM Id 15 P0
3/1/2011 5:01:00 AM-3/1/2011 5:31:00 AM Id 16 P1
3/1/2011 5:02:00 AM-3/1/2011 5:32:00 AM Id 17 P2
3/1/2011 6:00:00 AM-3/1/2011 6:30:00 AM Id 18 P3
3/1/2011 6:01:00 AM-3/1/2011 6:31:00 AM Id 19 P4

作业：
2011 年 3 月 1 日 12:00:00 AM-2011 年 3 月 1 日 12:30:00 AM Id 0 P0 C0
3/1/2011 12:01:00 AM-3/1/2011 12:31:00 AM Id 1 P1 C1
3/1/2011 1:00:00 AM-3/1/2011 1:30:00 AM Id 3 P3 C1
2011 年 3 月 1 日 1:02:00 AM-2011 年 3 月 1 日 1:32:00 AM Id 5 P0 C0
3/1/2011 2:00:00 AM-3/1/2011 2:30:00 AM Id 6 P1 C0
3/1/2011 2:01:00 AM-3/1/2011 2:31:00 AM Id 7 P2 C1
2011 年 3 月 1 日 3:01:00 AM-2011 年 3 月 1 日 3:31:00 AM Id 10 P0 C0
3/1/2011 3:02:00 AM-3/1/2011 3:32:00 AM Id 11 P1 C1
3/1/2011 4:00:00 AM-3/1/2011 4:30:00 AM Id 12 P2 C0
3/1/2011 4:01:00 AM-3/1/2011 4:31:00 AM Id 13 P3 C1
3/1/2011 5:00:00 AM-3/1/2011 5:30:00 AM Id 15 P0 C0

总比较数：1,443,556.00
按任意键继续

Answer 1

是否有理由使用 linq to 对象集合来完成此任务？我认为我会创建一个活动列表，将所有作业放入队列中，并在活动列表低于 10 时将下一个作业从队列中弹出，并将其放入活动列表中。跟踪哪个核心正在执行哪个任务并将队列中的下一个任务分配给最不繁忙的核心很容易。将完成的事件连接到作业或仅监视活动列表，您就会知道何时适合将另一个作业从队列中弹出并放入活动列表中。

Answer 2

我宁愿在一个循环中完成它。我的结果与你的不同。你安排了所有工作的 2/3。我的都安排好了。稍后我会添加解释。现在就出发去赴约了。

public class Job
{
    public static long Iterations;

    public int Id;
    public int Priority;
    public DateTime Begin;
    public DateTime End;

    public bool Overlaps(Job other)
    {
        Iterations++;
        return this.End > other.Begin && this.Begin < other.End;
    }
}

public class Assignment : IComparable<Assignment>
{
    public Job Job;
    public int Core;

    #region IComparable<Assignment> Members

    public int CompareTo(Assignment other)
    {
        return Job.Begin.CompareTo(other.Job.Begin);
    }

    #endregion
}

class Program
{
    static void Main(string[] args)
    {
        const int Jobs = 1000;
        const int Cores = 2;
        const int ConcurrentJobs = Cores + 1;
        const int Priorities = Cores + 3;

        DateTime startTime = new DateTime(2011, 3, 1, 0, 0, 0, 0);
        Console.WriteLine(string.Format("{0} Jobs x {1} Cores", Jobs, Cores));
        var timer = Stopwatch.StartNew();

        Console.WriteLine("Populating data");
        var jobs = new List<Job>();
        for (int jobId = 0; jobId < Jobs; jobId++)
        {
            var jobStart = startTime.AddHours(jobId / ConcurrentJobs).AddMinutes(jobId % ConcurrentJobs);
            jobs.Add(new Job() { Id = jobId, Priority = jobId % Priorities, Begin = jobStart, End = jobStart.AddHours(0.5) });
        }
        Console.WriteLine(string.Format("Completed in {0:n}ms", timer.ElapsedMilliseconds));
        timer.Reset();

        Console.WriteLine("Assigning Jobs to Cores");
        List<Assignment>[] assignments = new List<Assignment>[Cores];
        for (int core = 0; core < Cores; core++)
            assignments[core] = new List<Assignment>();

        Job[] lastJobs = new Job[Cores];
        foreach (Job j in jobs)
        {
            Job job = j;
            bool assigned = false;
            for (int core = 0; core < Cores; core++)
            {
                if (lastJobs[core] == null || !lastJobs[core].Overlaps(job))
                {
                    // Assign directly if no last job or no overlap with last job
                    lastJobs[core] = job;
                    assignments[core].Add(new Assignment { Job = job, Core = core });
                    assigned = true;
                    break;
                }
                else if (job.Priority > lastJobs[core].Priority)
                {
                    // Overlap and higher priority, so we replace
                    Job temp = lastJobs[core];
                    lastJobs[core] = job;
                    job = temp; // Will try to later assign to other core

                    assignments[core].Add(new Assignment { Job = job, Core = core });
                    assigned = true;
                    break;
                }
            }
            if (!assigned)
            {
                // TODO: What to do if not assigned? Your code seems to just ignore them
            }
        }
        List<Assignment> merged = new List<Assignment>();
        for (int core = 0; core < Cores; core++)
            merged.AddRange(assignments[core]);
        merged.Sort();
        Console.WriteLine(string.Format("Completed in {0:n}ms", timer.ElapsedMilliseconds));
        timer.Reset();

        Console.WriteLine(string.Format("\nTotal Comparisons: {0:n}", Job.Iterations));
        Job.Iterations = 0; // Reset to count again

        {
            IEnumerable<Assignment> assignments2 = null;
            for (int core = 0; core < Cores; core++)
            {


                // avoid modified closures by creating local variables
                int localCore = core;
                var localAssignments = assignments2;

                // Step 1: Determine the remaining jobs
                var remainingJobs = localAssignments == null ?
                                                    jobs :
                                                    from j in jobs where !(from a in localAssignments select a.Job).Contains(j) select j;

                // Step 2: Assign the top priority job in any time-slot to the core
                var assignmentsForCore = from s1 in remainingJobs
                                         where
                                             (from s2 in remainingJobs
                                              where s1.Overlaps(s2)
                                              orderby s2.Priority
                                              select s2).First().Equals(s1)
                                         select new Assignment { Job = s1, Core = localCore };

                // Step 3: Accumulate the results (unfortunately requires a .ToList() to avoid massive over-joins)
                assignments2 = assignments2 == null ? assignmentsForCore.ToList() : assignments2.Concat(assignmentsForCore.ToList());
            }

            // This is where I'd like to Execute the query one single time across all cores, but have to do intermediate steps to avoid massive-over-joins
            assignments2 = assignments2.ToList();

            Console.WriteLine(string.Format("Completed in {0:n}ms", timer.ElapsedMilliseconds));
            Console.WriteLine("\nJobs:");
            foreach (var job in jobs.Take(20))
            {
                Console.WriteLine(string.Format("{0}-{1} Id {2} P{3}", job.Begin, job.End, job.Id, job.Priority));
            }

            Console.WriteLine("\nAssignments:");
            foreach (var assignment in assignments2.OrderBy(a => a.Job.Begin).Take(10))
            {
                Console.WriteLine(string.Format("{0}-{1} Id {2} P{3} C{4}", assignment.Job.Begin, assignment.Job.End, assignment.Job.Id, assignment.Job.Priority, assignment.Core));
            }

            if (merged.Count != assignments2.Count())
                System.Console.WriteLine("Difference count {0}, {1}", merged.Count, assignments2.Count());
            for (int i = 0; i < merged.Count() && i < assignments2.Count(); i++)
            {
                var a2 = assignments2.ElementAt(i);
                var a = merged[i];
                if (a.Job.Id != a2.Job.Id)
                    System.Console.WriteLine("Difference at {0} {1} {2}", i, a.Job.Begin, a2.Job.Begin);
                if (i % 100 == 0) Console.ReadKey();
            }
        }


        Console.WriteLine(string.Format("\nTotal Comparisons: {0:n}", Job.Iterations));

        Console.WriteLine("Any key to continue");
        Console.ReadKey();
    }
}

---

由于重大错误而被删除。重做一下..:P