Optimization

The Elevator Problem The Elevator Problem is a classic scheduling and optimization challenge that models how multiple elevators coordinate to serve passengers efficiently. It demonstrates load balancing, scheduling algorithms, optimization trade-offs, and decentralized coordination. Unlike many concurrency problems, it focuses on real-time decision-making and multi-objective optimization. The Scenario A building has: N elevators moving between floors M floors Passengers arriving at random floors with random destinations Call buttons (up/down) on each floor Destination buttons inside each elevator The goals: ...

In 2006, Netflix announced a challenge: improve our recommendation algorithm by 10%, win $1 million. The Netflix Prize became one of the most famous machine learning competitions ever. Thousands of teams from around the world competed for three years. In 2009, team “BellKor’s Pragmatic Chaos” won. They’d built an algorithm that was 10.06% better than Netflix’s existing system. Netflix awarded the $1 million prize. The press celebrated the triumph of data science. ...

Introduction: The Memory Wall Modern LLMs can process context windows of 100K+ tokens. But there’s a hidden cost: the KV cache. As context grows, the memory required to store key-value pairs in attention explodes quadratically. This creates a bottleneck: Memory: KV cache can consume 10-100× more memory than model weights Bandwidth: Moving KV cache data becomes the primary latency source Cost: Serving long-context models requires expensive high-memory GPUs Two innovations address this: Grouped Query Attention (GQA) and Multi-Head Latent Attention (MLA). They reduce KV cache size by 4-8× while maintaining quality. ...