Algorithmic Efficiency Benchmarks

An empirical analysis of competitive programming optimization techniques

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📚 Overview

This repository benchmarks highly-optimized graph and tree algorithms commonly found in competitive programming (USACO Platinum, Codeforces) against standard textbook implementations. The goal is to empirically quantify why these micro-optimizations matter for high-performance computing.

Algorithms Analyzed

Problem Domain	Optimized Implementation	Optimization Techniques
Maximum Matching	Edmonds' Blossom Algorithm	Static memory allocation, BFS queue reuse, lazy LCA computation
Probabilistic DP	Divide & Conquer + Polynomial Convolution	Modular arithmetic, segment tagging, memory-efficient recursion
Tree Queries	Binary Lifting + LCA	Precomputed sparse tables, matrix exponentiation for path aggregation

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📁 Repository Structure

Algorithmic-Efficiency-Benchmarks/
├── optimized/           # Competition-grade implementations
│   ├── edmonds_blossom.cpp
│   ├── dc_polynomial_dp.cpp
│   └── tree_binary_lifting.cpp
├── naive/               # Textbook-style implementations
│   ├── brute_matching.cpp
│   ├── simulation_dp.cpp
│   └── dfs_tree_query.cpp
├── benchmarks/          # Performance testing infrastructure
│   ├── benchmark.py     # Main benchmark runner
│   └── generate_graphs.py
├── data/                # Test datasets of varying sizes
├── results/             # Benchmark outputs and visualizations
└── paper/               # Technical analysis paper

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🚀 Quick Start

Prerequisites

• C++17 compiler (g++ 9+ or clang++ 10+)
• Python 3.8+ with matplotlib, numpy

Run Benchmarks

# Generate test data
python benchmarks/generate_graphs.py

# Compile implementations
make all

# Run benchmarks
python benchmarks/benchmark.py

# View results
open results/performance_comparison.png

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📊 Key Findings

Our benchmarks show the optimized implementations achieve:

• 100-400x speedup on dense graphs (N > 1000)
• 50% memory reduction through static allocation
• Linear scaling vs exponential for naive approaches

See Technical Paper for detailed analysis.

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🔬 Methodology

This study follows established practices for algorithm benchmarking:

1. Controlled Environment: All tests run on identical hardware with CPU frequency locked
2. Statistical Validity: Each test runs 10+ iterations, reporting median times
3. Fair Comparison: Both implementations use identical I/O and data structures where possible

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📄 Citation

If you use this work in academic research, please cite:

@misc{algorithmic-efficiency-benchmarks,
  title={Benchmarking Competitive Programming Optimization Techniques},
  author=Daniyal Kadirbekov,
  year={2026},
  howpublished={\url{https://github.com/SoDonik/Algorithmic-Efficiency-Benchmarks}}
}

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📜 License

MIT License - See LICENSE for details.

Note: The optimized implementations are adapted from publicly available competitive programming solutions for educational analysis purposes only.