# 5.25 Case Studies

# 5.25 Case Studies

## Problem

You need to see how hash-based structures behave in complete systems rather than isolated operations. Real performance and correctness issues usually appear only when hashing interacts with full workflows: streaming data, graphs, caches, and distributed systems.

This section consolidates patterns from previous recipes into concrete end-to-end designs.

## Case Study 1: Frequency Analysis Pipeline

You need to compute frequencies over a large stream of events.

### Design

Use a counting map.

```text id="c1q8mx"
freq = empty map

for event in stream:
    put(freq, event, get(freq, event, 0) + 1)
```

### Discussion

This is the canonical use of a hash map: aggregation over streaming input. The performance depends primarily on hash distribution and memory locality. If the event space is large, resizing dominates early cost; after stabilization, updates become constant time.

### Failure modes

* skewed keys create hot buckets
* memory growth becomes unbounded
* high-cardinality streams dominate space

---

## Case Study 2: Web Cache

You need to cache HTTP responses by request key.

### Design

Use a hash map with eviction policy.

```text id="w8n2kd"
cache: Map<Request, Response>
```

Optionally combine with LRU tracking.

```text id="k3v9xp"
on get(key):
    if key in cache:
        move_to_recent(key)
        return cache[key]
```

### Discussion

Hashing provides fast lookup; eviction ensures bounded memory. The main challenge is coordinating map updates with eviction structure consistency.

### Failure modes

* stale entries after eviction desync
* memory leaks from missing removal
* inconsistent key normalization

---

## Case Study 3: Graph Traversal

You need to avoid revisiting nodes in BFS or DFS.

### Design

Use a hash set.

```text id="g7m3qv"
visited = empty set

for node in traversal:
    if not contains(visited, node):
        insert(visited, node)
        process(node)
```

### Discussion

The set enforces correctness by preventing cycles and redundant exploration. Performance depends on fast membership checks and good hashing of node identifiers.

### Failure modes

* missing visited marking leads to infinite loops
* mutable node identifiers break correctness
* poor hashing slows traversal dramatically

---

## Case Study 4: Distributed Partitioning

You need to distribute keys across machines.

### Design

Use consistent hashing.

```text id="d9v2kq"
node = ring_successor(hash(key))
```

### Discussion

The key property is stability under node changes. Only a small fraction of keys move when nodes are added or removed.

### Failure modes

* uneven node distribution without virtual nodes
* inconsistent hashing across services
* missing ring synchronization

---

## Case Study 5: Deduplication at Scale

You need to remove duplicates from a massive dataset.

### Design

Use hash set or hybrid approximate structure.

```text id="p6c8rz"
seen = empty set

for item in stream:
    if not contains(seen, item):
        insert(seen, item)
        emit(item)
```

For very large datasets, switch to probabilistic filtering:

* Bloom filter for memory reduction
* or hybrid Bloom + set for accuracy control

### Discussion

This pattern is dominated by memory constraints rather than compute. Hashing ensures constant-time checks, but memory growth is the limiting factor.

### Failure modes

* unbounded memory growth
* false positives in approximate structures
* inconsistent hashing across partitions

---

## Case Study 6: Join in Data Processing

You need to combine two datasets by key.

### Design

Hash join.

```text id="j2m9kv"
build table from smaller dataset
probe with larger dataset
```

### Discussion

The build-probe separation is critical. Hashing transforms relational joins into expected linear-time operations.

### Failure modes

* building on the wrong side (memory blowup)
* skewed keys causing large buckets
* output explosion from many-to-many joins

---

## Case Study 7: Log Aggregation

You need to aggregate metrics from logs in real time.

### Design

Combine hashing with counting maps.

```text id="l4q7nz"
metrics = Map<metric_key, counter>

for log in stream:
    metrics[log.key] += 1
```

### Discussion

This is a hybrid of counting maps and streaming systems. The key challenge is throughput and memory pressure.

### Failure modes

* high-cardinality metric explosion
* uneven key distribution
* slow rehashing during bursts

---

## Synthesis

Across all case studies, hash-based structures share recurring constraints:

* correctness depends on equality consistency
* performance depends on hash distribution
* scalability depends on memory control and resizing
* stability depends on avoiding pathological input patterns

Hashing is not a single algorithm. It is a coordination layer between data, memory, and access patterns.

---

If you want, the next step is to close the cookbook with a final chapter on “design rules for selecting hash strategies,” or move into a different topic like trees, graphs, or dynamic programming cookbooks.