SqrtSpace SpaceTime for .NET

Memory-efficient algorithms and data structures for .NET using Williams' √n space-time tradeoffs. Reduce memory usage by 90-99% with minimal performance impact.

Paper Repository: git.marketally.com/sqrtspace/sqrtspace-paper

Quick Start

# Core functionality
dotnet add package SqrtSpace.SpaceTime.Core

# LINQ extensions
dotnet add package SqrtSpace.SpaceTime.Linq

# Adaptive collections
dotnet add package SqrtSpace.SpaceTime.Collections

# Entity Framework Core integration
dotnet add package SqrtSpace.SpaceTime.EntityFramework

# ASP.NET Core middleware
dotnet add package SqrtSpace.SpaceTime.AspNetCore

# Roslyn analyzers
dotnet add package SqrtSpace.SpaceTime.Analyzers

# Additional packages
dotnet add package SqrtSpace.SpaceTime.Caching
dotnet add package SqrtSpace.SpaceTime.Distributed
dotnet add package SqrtSpace.SpaceTime.Diagnostics
dotnet add package SqrtSpace.SpaceTime.Scheduling
dotnet add package SqrtSpace.SpaceTime.Pipeline
dotnet add package SqrtSpace.SpaceTime.Configuration
dotnet add package SqrtSpace.SpaceTime.Serialization
dotnet add package SqrtSpace.SpaceTime.MemoryManagement

What's Included

1. Core Library

Foundation for all SpaceTime optimizations:

using SqrtSpace.SpaceTime.Core;

// Calculate optimal buffer sizes
int bufferSize = SpaceTimeCalculator.CalculateSqrtInterval(dataSize);

// Get memory hierarchy information
var hierarchy = MemoryHierarchy.GetCurrent();
Console.WriteLine($"L1 Cache: {hierarchy.L1CacheSize:N0} bytes");
Console.WriteLine($"L2 Cache: {hierarchy.L2CacheSize:N0} bytes");
Console.WriteLine($"Available RAM: {hierarchy.AvailableMemory:N0} bytes");

// Use external storage for large data
using var storage = new ExternalStorage<Record>("data.tmp");
await storage.AppendAsync(records);

2. Memory-Aware LINQ Extensions

Transform memory-hungry LINQ operations:

using SqrtSpace.SpaceTime.Linq;

// Standard LINQ - loads all 10M items into memory
var sorted = millionItems
    .OrderBy(x => x.Date)
    .ToList(); // 800MB memory

// SpaceTime LINQ - uses √n memory
var sorted = millionItems
    .OrderByExternal(x => x.Date)
    .ToList(); // 25MB memory (97% less!)

// Process in optimal batches
await foreach (var batch in largeQuery.BatchBySqrtNAsync())
{
    await ProcessBatch(batch);
}

// External joins for large datasets
var results = customers
    .JoinExternal(orders, c => c.Id, o => o.CustomerId, 
        (c, o) => new { Customer = c, Order = o })
    .ToList();

3. Adaptive Collections

Collections that automatically switch implementations based on size:

using SqrtSpace.SpaceTime.Collections;

// Automatically adapts: Array → Dictionary → B-Tree → External storage
var adaptiveMap = new AdaptiveDictionary<string, Customer>();

// Starts as array (< 16 items)
adaptiveMap["user1"] = customer1;

// Switches to Dictionary (< 10K items)
for (int i = 0; i < 5000; i++)
    adaptiveMap[$"user{i}"] = customers[i];

// Switches to B-Tree (< 1M items)
// Then to external storage (> 1M items) with √n memory

// Adaptive lists with external sorting
var list = new AdaptiveList<Order>();
list.AddRange(millionOrders);
list.Sort(); // Automatically uses external sort if needed

4. Entity Framework Core Optimizations

Optimize EF Core for large datasets:

services.AddDbContext<AppDbContext>(options =>
{
    options.UseSqlServer(connectionString)
           .UseSpaceTimeOptimizer(opt =>
           {
               opt.EnableSqrtNChangeTracking = true;
               opt.BufferPoolStrategy = BufferPoolStrategy.SqrtN;
               opt.EnableQueryCheckpointing = true;
           });
});

// Query with √n memory usage
var results = await dbContext.Orders
    .Where(o => o.Status == "Pending")
    .ToListWithSqrtNMemoryAsync();

// Process in optimal batches
await foreach (var batch in dbContext.Customers.BatchBySqrtNAsync())
{
    await ProcessCustomerBatch(batch);
}

// Optimized change tracking
using (dbContext.BeginSqrtNTracking())
{
    // Make changes to thousands of entities
    await dbContext.BulkUpdateAsync(entities);
}

5. ASP.NET Core Streaming

Stream large responses efficiently:

[HttpGet("large-dataset")]
[SpaceTimeStreaming(ChunkStrategy = ChunkStrategy.SqrtN)]
public async IAsyncEnumerable<DataItem> GetLargeDataset()
{
    // Automatically chunks response using √n sizing
    await foreach (var item in repository.GetAllAsync())
    {
        yield return item;
    }
}

// In Program.cs
builder.Services.AddSpaceTime(options =>
{
    options.EnableCheckpointing = true;
    options.EnableStreaming = true;
    options.DefaultChunkSize = SpaceTimeDefaults.SqrtN;
});

app.UseSpaceTime();
app.UseSpaceTimeEndpoints();

6. Memory-Aware Caching

Intelligent caching with hot/cold storage:

using SqrtSpace.SpaceTime.Caching;

// Configure caching
services.AddSpaceTimeCaching(options =>
{
    options.MaxHotMemory = 100 * 1024 * 1024; // 100MB hot cache
    options.EnableColdStorage = true;
    options.ColdStoragePath = "/tmp/cache";
    options.EvictionStrategy = EvictionStrategy.SqrtN;
});

// Use the cache
public class ProductService
{
    private readonly ISpaceTimeCache<string, Product> _cache;
    
    public async Task<Product> GetProductAsync(string id)
    {
        return await _cache.GetOrAddAsync(id, async () =>
        {
            // Expensive database query
            return await _repository.GetProductAsync(id);
        });
    }
}

7. Distributed Processing

Coordinate work across multiple nodes:

using SqrtSpace.SpaceTime.Distributed;

// Configure distributed coordinator
services.AddSpaceTimeDistributed(options =>
{
    options.NodeId = Environment.MachineName;
    options.CoordinationEndpoint = "redis://coordinator:6379";
});

// Use distributed processing
public class DataProcessor
{
    private readonly ISpaceTimeCoordinator _coordinator;
    
    public async Task ProcessLargeDatasetAsync(string datasetId)
    {
        // Get optimal partition for this node
        var partition = await _coordinator.RequestPartitionAsync(
            datasetId, estimatedSize: 10_000_000);
        
        // Process only this node's portion
        await foreach (var item in GetPartitionData(partition))
        {
            await ProcessItem(item);
            await _coordinator.ReportProgressAsync(partition.Id, 1);
        }
    }
}

8. Diagnostics and Monitoring

Comprehensive diagnostics with OpenTelemetry:

using SqrtSpace.SpaceTime.Diagnostics;

// Configure diagnostics
services.AddSpaceTimeDiagnostics(options =>
{
    options.EnableMetrics = true;
    options.EnableTracing = true;
    options.EnableMemoryTracking = true;
});

// Monitor operations
public class ImportService
{
    private readonly ISpaceTimeDiagnostics _diagnostics;
    
    public async Task ImportDataAsync(string filePath)
    {
        using var operation = _diagnostics.StartOperation(
            "DataImport", OperationType.BatchProcessing);
        
        operation.SetTag("file.path", filePath);
        operation.SetTag("file.size", new FileInfo(filePath).Length);
        
        try
        {
            await ProcessFile(filePath);
            operation.RecordSuccess();
        }
        catch (Exception ex)
        {
            operation.RecordError(ex);
            throw;
        }
    }
}

9. Memory-Aware Task Scheduling

Schedule tasks based on memory availability:

using SqrtSpace.SpaceTime.Scheduling;

// Configure scheduler
services.AddSpaceTimeScheduling(options =>
{
    options.MaxMemoryPerTask = 50 * 1024 * 1024; // 50MB per task
    options.EnableMemoryThrottling = true;
});

// Schedule memory-intensive tasks
public class BatchProcessor
{
    private readonly ISpaceTimeTaskScheduler _scheduler;
    
    public async Task ProcessBatchesAsync(IEnumerable<Batch> batches)
    {
        var tasks = batches.Select(batch => 
            _scheduler.ScheduleAsync(async () =>
            {
                await ProcessBatch(batch);
            }, 
            estimatedMemory: batch.EstimatedMemoryUsage,
            priority: TaskPriority.Normal));
        
        await Task.WhenAll(tasks);
    }
}

10. Data Pipeline Framework

Build memory-efficient data pipelines:

using SqrtSpace.SpaceTime.Pipeline;

// Build a pipeline
var pipeline = pipelineFactory.CreatePipeline<InputData, OutputData>("ImportPipeline")
    .AddTransform("Parse", async (input, ct) => 
        await ParseData(input))
    .AddBatch("Validate", async (batch, ct) => 
        await ValidateBatch(batch))
    .AddFilter("FilterInvalid", data => 
        data.IsValid)
    .AddCheckpoint("SaveProgress")
    .AddParallel("Enrich", async (data, ct) => 
        await EnrichData(data), maxConcurrency: 4)
    .Build();

// Execute pipeline
var result = await pipeline.ExecuteAsync(inputData);

11. Configuration and Policy System

Centralized configuration management:

using SqrtSpace.SpaceTime.Configuration;

// Configure SpaceTime
services.AddSpaceTimeConfiguration(configuration);

// Define policies
services.Configure<SpaceTimeConfiguration>(options =>
{
    options.Memory.MaxMemory = 1_073_741_824; // 1GB
    options.Memory.ExternalAlgorithmThreshold = 0.7; // Switch at 70%
    options.Algorithms.Policies["Sort"] = new AlgorithmPolicy
    {
        PreferExternal = true,
        SizeThreshold = 1_000_000
    };
});

// Use policy engine
public class DataService
{
    private readonly IPolicyEngine _policyEngine;
    
    public async Task<ProcessingStrategy> DetermineStrategyAsync(long dataSize)
    {
        var context = new PolicyContext
        {
            OperationType = "DataProcessing",
            DataSize = dataSize,
            AvailableMemory = GC.GetTotalMemory(false)
        };
        
        var result = await _policyEngine.EvaluateAsync(context);
        return result.ShouldProceed 
            ? ProcessingStrategy.Continue 
            : ProcessingStrategy.Defer;
    }
}

12. Serialization Optimizers

Memory-efficient serialization with streaming:

using SqrtSpace.SpaceTime.Serialization;

// Configure serialization
services.AddSpaceTimeSerialization(builder =>
{
    builder.UseFormat(SerializationFormat.MessagePack)
           .ConfigureCompression(enable: true, level: 6)
           .ConfigureMemoryLimits(100 * 1024 * 1024); // 100MB
});

// Stream large collections
public class ExportService
{
    private readonly StreamingSerializer<Customer> _serializer;
    
    public async Task ExportCustomersAsync(string filePath)
    {
        await _serializer.SerializeToFileAsync(
            GetCustomersAsync(),
            filePath,
            options: new SerializationOptions
            {
                EnableCheckpointing = true,
                BufferSize = 0 // Auto √n sizing
            },
            progress: new Progress<SerializationProgress>(p =>
            {
                Console.WriteLine($"Exported {p.ItemsProcessed:N0} items");
            }));
    }
}

13. Memory Pressure Handling

Automatic response to memory pressure:

using SqrtSpace.SpaceTime.MemoryManagement;

// Configure memory management
services.AddSpaceTimeMemoryManagement(options =>
{
    options.EnableAutomaticHandling = true;
    options.CheckInterval = TimeSpan.FromSeconds(5);
});

// Add custom handler
services.AddMemoryPressureHandler<CustomCacheEvictionHandler>();

// Monitor memory pressure
public class MemoryAwareService
{
    private readonly IMemoryPressureMonitor _monitor;
    
    public MemoryAwareService(IMemoryPressureMonitor monitor)
    {
        _monitor = monitor;
        _monitor.PressureEvents.Subscribe(OnMemoryPressure);
    }
    
    private void OnMemoryPressure(MemoryPressureEvent e)
    {
        if (e.CurrentLevel >= MemoryPressureLevel.High)
        {
            // Reduce memory usage
            TrimCaches();
            ForceGarbageCollection();
        }
    }
}

14. Checkpointing for Fault Tolerance

Add automatic checkpointing to long-running operations:

[EnableCheckpoint(Strategy = CheckpointStrategy.SqrtN)]
public async Task<ImportResult> ImportLargeDataset(string filePath)
{
    var checkpoint = HttpContext.Features.Get<ICheckpointFeature>();
    var results = new List<Record>();
    
    await foreach (var record in ReadRecordsAsync(filePath))
    {
        var processed = await ProcessRecord(record);
        results.Add(processed);
        
        // Automatically checkpoints every √n iterations
        if (checkpoint.ShouldCheckpoint())
        {
            await checkpoint.SaveStateAsync(results);
        }
    }
    
    return new ImportResult(results);
}

15. Roslyn Analyzers

Get compile-time suggestions for memory optimizations:

// Analyzer warning: ST001 - Large allocation detected
var allOrders = await dbContext.Orders.ToListAsync(); // Warning

// Quick fix applied:
var allOrders = await dbContext.Orders.ToListWithSqrtNMemoryAsync(); // Fixed

// Analyzer warning: ST002 - Inefficient LINQ operation
var sorted = items.OrderBy(x => x.Id).ToList(); // Warning

// Quick fix applied:
var sorted = items.OrderByExternal(x => x.Id).ToList(); // Fixed

Real-World Performance

Benchmarks on .NET 8.0:

Operation	Standard	SpaceTime	Memory Reduction	Time Overhead
Sort 10M items	800MB, 1.2s	25MB, 1.8s	97%	50%
LINQ GroupBy 1M	120MB, 0.8s	3.5MB, 1.1s	97%	38%
EF Core Query 100K	200MB, 2.1s	14MB, 2.4s	93%	14%
Stream 1GB JSON	1GB, 5s	32MB, 5.5s	97%	10%
Cache 1M items	400MB	35MB hot + disk	91%	5%
Distributed sort	N/A	50MB per node	95%	20%

When to Use

Perfect for:

• Large dataset processing (> 100K items)
• Memory-constrained environments (containers, serverless)
• Reducing cloud costs (smaller instances)
• Import/export operations
• Batch processing
• Real-time systems with predictable memory
• Distributed data processing
• Long-running operations requiring fault tolerance

Not ideal for:

• Small datasets (< 1000 items)
• Ultra-low latency requirements (< 10ms)
• Simple CRUD operations
• CPU-bound calculations without memory pressure

Configuration

Global Configuration

// In Program.cs
services.Configure<SpaceTimeConfiguration>(config =>
{
    // Memory settings
    config.Memory.MaxMemory = 1_073_741_824; // 1GB
    config.Memory.BufferSizeStrategy = BufferSizeStrategy.Sqrt;
    
    // Algorithm selection
    config.Algorithms.EnableAdaptiveSelection = true;
    config.Algorithms.MinExternalAlgorithmSize = 10_000_000; // 10MB
    
    // Performance tuning
    config.Performance.EnableParallelism = true;
    config.Performance.MaxDegreeOfParallelism = Environment.ProcessorCount;
    
    // Storage settings
    config.Storage.DefaultStorageDirectory = "/tmp/spacetime";
    config.Storage.EnableCompression = true;
    
    // Features
    config.Features.EnableCheckpointing = true;
    config.Features.EnableAdaptiveDataStructures = true;
});

Environment Variables

Configure via environment variables:

# Memory settings
SPACETIME_MAX_MEMORY=1073741824
SPACETIME_MEMORY_THRESHOLD=0.7

# Performance settings
SPACETIME_ENABLE_PARALLEL=true
SPACETIME_MAX_PARALLELISM=8

# Storage settings
SPACETIME_STORAGE_DIR=/tmp/spacetime
SPACETIME_ENABLE_COMPRESSION=true

Per-Operation Configuration

// Custom buffer size
var sorted = data.OrderByExternal(x => x.Id, bufferSize: 10000);

// Custom checkpoint interval  
var checkpoint = new CheckpointManager(strategy: CheckpointStrategy.Linear);

// Force specific implementation
var list = new AdaptiveList<Order>(strategy: AdaptiveStrategy.ForceExternal);

// Configure pipeline
var pipeline = builder.Configure(config =>
{
    config.ExpectedItemCount = 1_000_000;
    config.EnableCheckpointing = true;
    config.DefaultTimeout = TimeSpan.FromMinutes(30);
});

How It Works

Based on Williams' theoretical result that TIME[t] ⊆ SPACE[√(t log t)]:

1. Memory Reduction: Use O(√n) memory instead of O(n)
2. External Storage: Spill to disk when memory limit reached
3. Optimal Chunking: Process data in √n-sized chunks
4. Adaptive Strategies: Switch algorithms based on data size
5. Distributed Coordination: Split work across nodes
6. Memory Pressure Handling: Automatic response to low memory

Examples

Processing Large CSV

[HttpPost("import-csv")]
[EnableCheckpoint]
public async Task<IActionResult> ImportCsv(IFormFile file)
{
    var pipeline = _pipelineFactory.CreatePipeline<string, Record>("CsvImport")
        .AddTransform("Parse", line => ParseCsvLine(line))
        .AddBatch("Validate", async batch => await ValidateRecords(batch))
        .AddCheckpoint("Progress")
        .AddTransform("Save", async record => await SaveRecord(record))
        .Build();
    
    var lines = ReadCsvLines(file.OpenReadStream());
    var result = await pipeline.ExecuteAsync(lines);
    
    return Ok(new { ProcessedCount = result.ProcessedCount });
}

Optimized Data Export

[HttpGet("export")]
[SpaceTimeStreaming]
public async IAsyncEnumerable<CustomerExport> ExportCustomers()
{
    // Process customers in √n batches with progress
    var totalCount = await dbContext.Customers.CountAsync();
    var batchSize = SpaceTimeCalculator.CalculateSqrtInterval(totalCount);
    
    await foreach (var batch in dbContext.Customers
        .OrderBy(c => c.Id)
        .BatchAsync(batchSize))
    {
        foreach (var customer in batch)
        {
            yield return new CustomerExport
            {
                Id = customer.Id,
                Name = customer.Name,
                TotalOrders = await GetOrderCount(customer.Id)
            };
        }
    }
}

Memory-Aware Background Job

public class DataProcessingJob : IHostedService
{
    private readonly ISpaceTimeTaskScheduler _scheduler;
    private readonly IMemoryPressureMonitor _memoryMonitor;
    
    public async Task ExecuteAsync(CancellationToken cancellationToken)
    {
        // Schedule based on memory availability
        await _scheduler.ScheduleAsync(async () =>
        {
            if (_memoryMonitor.CurrentPressureLevel > MemoryPressureLevel.Medium)
            {
                // Use external algorithms
                await ProcessDataExternal();
            }
            else
            {
                // Use in-memory algorithms
                await ProcessDataInMemory();
            }
        }, 
        estimatedMemory: 100 * 1024 * 1024, // 100MB
        priority: TaskPriority.Low);
    }
}

Contributing

We welcome contributions! Please see our Contributing Guide.

License

Apache 2.0 - See LICENSE for details.

Links

• NuGet Packages
• Git Repository

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Making theoretical computer science practical for .NET developers