parallel-execution

What this skill does

# Parallel Execution Patterns for Cognitive Reasoning

**Purpose**: Accelerate and improve cognitive reasoning by executing independent tasks simultaneously. Parallel execution can achieve 2-4x efficiency gains and 70% faster convergence when applied appropriately to reasoning patterns like ToT, BoT, HE, and AT.

## When to Use Parallel Execution

**Use parallel execution when:**
- Problem decomposes into independent sub-problems
- Multiple solution approaches need exploration (BoT, ToT branching)
- High confidence required (ensemble methods)
- Multiple hypotheses need simultaneous testing (HE)
- Time permits depth but sequential execution is unnecessary
- Cross-domain analogies need parallel investigation (AT)

**Do not parallelize when:**
- Steps have sequential dependencies (use SRC instead)
- Each step depends on previous results
- Problem is inherently linear (debugging traces)
- Resource constraints limit concurrent execution
- Merge strategy is undefined

**Parallelization Decision Matrix:**

| Problem Characteristic | Parallelize? | Rationale |
|------------------------|--------------|-----------|
| Independent sub-problems | Yes | No dependencies, safe to parallelize |
| Multiple valid approaches | Yes | BoT/ToT branches are independent |
| Hypothesis testing | Yes | HE hypotheses can test in parallel |
| Sequential reasoning | No | SRC chains have dependencies |
| Cause-effect tracing | No | Effects depend on causes |
| Resource gathering | Yes | Independent evidence sources |

---

## Core Patterns

### Pattern 1: Dynamic Parallel Tree Search (DPTS)

**Efficiency**: 2-4x improvement, 70% faster convergence

**Description**: Adaptive parallel exploration that dynamically allocates resources to promising branches while pruning unpromising ones. Unlike static parallel search, DPTS reallocates workers as branches are evaluated.

**Key Mechanisms:**
- **Dynamic worker allocation**: More workers on promising branches
- **Adaptive pruning thresholds**: Thresholds adjust based on best-found confidence
- **Early termination**: Stop exploring when confidence exceeds threshold
- **Resource rebalancing**: Move workers from exhausted/pruned branches

**Integration with ToT:**

```markdown
## DPTS + Tree of Thoughts

### Phase 1: Initial Parallel Expansion
- Spawn N workers for Level 0 branches (N = 5-10)
- Each worker explores one branch independently
- Workers report confidence scores as they complete

### Phase 2: Dynamic Reallocation
- As Level 0 completes, rank branches by score
- Top 2 branches get 3 workers each for Level 1
- Remaining branches get 1 worker each
- Prune branches below dynamic threshold

### Phase 3: Convergence
- Continue reallocation until:
  - Winning branch confidence > 85%
  - OR all branches at Level 4+
  - OR diminishing returns detected

### Pruning Threshold Formula
dynamic_threshold = max(0.40, best_confidence - 0.30)
```

**Example DPTS Execution:**

```
Level 0: 5 branches, 5 workers (parallel)
├─ Branch A: 75% confidence (3 workers assigned for L1)
├─ Branch B: 68% confidence (2 workers assigned for L1)
├─ Branch C: 52% confidence (1 worker, threshold = 45%)
├─ Branch D: 48% confidence (1 worker, threshold = 45%)
└─ Branch E: 35% confidence (PRUNED, below threshold)

Level 1: 8 workers reallocated
├─ A.1, A.2, A.3: parallel (3 workers)
├─ B.1, B.2: parallel (2 workers)
├─ C.1: sequential (1 worker)
└─ D.1: sequential (1 worker)

Best found: A.2 at 82% → New threshold: 52%
→ Branch D PRUNED (48% < 52%)
→ 1 worker reallocated to Branch A
```

---

### Pattern 2: Branch-Solve-Merge (BSM)

**Description**: Three-phase pattern that decomposes problems, solves sub-problems in parallel, then merges results. Ideal for problems that can be cleanly partitioned.

**Phases:**

```markdown
## Branch Phase (Decomposition)
1. Analyze problem structure
2. Identify independent sub-problems
3. Define interfaces between sub-problems
4. Create sub-problem specifications

## Solve Phase (Parallel Execution)
1. Spawn worker per sub-problem
2. Each worker solves independently
3. Workers report partial solutions
4. Monitor for blocking dependencies

## Merge Phase (Aggregation)
1. Collect all partial solutions
2. Apply merge strategy (see below)
3. Resolve conflicts
4. Synthesize final solution
```

**Merge Strategies:**

| Strategy | When to Use | Method |
|----------|-------------|--------|
| **Consensus** | Multiple workers on same problem | Majority agreement |
| **Voting** | Competing approaches | Weighted score aggregation |
| **Aggregation** | Complementary results | Union with deduplication |
| **Synthesis** | Conflicting valid results | Dialectical resolution |

**BSM Example - Architecture Decision:**

```markdown
## Branch: "Design authentication system"
Sub-problems:
1. Token format selection (JWT vs Session vs API Key)
2. Storage strategy (Redis vs DB vs Memory)
3. Security requirements (MFA, encryption, audit)
4. Performance requirements (latency, throughput)

## Solve: 4 parallel workers
Worker 1: Evaluates token formats → JWT (85%)
Worker 2: Evaluates storage → Redis (78%)
Worker 3: Analyzes security → MFA required (92%)
Worker 4: Benchmarks performance → < 50ms needed (88%)

## Merge: Aggregation strategy
- JWT + Redis + MFA + 50ms latency
- Check compatibility: All compatible
- Synthesize: "JWT tokens stored in Redis with MFA, target 50ms"
```

---

### Pattern 3: Mixture of Agents (MoA)

**Description**: Layered architecture where proposer agents generate solutions and aggregator agents synthesize them. Mimics ensemble learning for improved robustness.

**Architecture:**

```
┌─────────────────────────────────────────────────┐
│                 Aggregator Layer                 │
│  (Synthesizes proposals, resolves conflicts)    │
└────────────────────┬────────────────────────────┘
                     │ Proposals flow up
┌─────────────────────────────────────────────────┐
│                 Proposer Layer                   │
│  ┌─────────┐ ┌─────────┐ ┌─────────┐           │
│  │Proposer1│ │Proposer2│ │Proposer3│  ...      │
│  │ (ToT)   │ │ (BoT)   │ │ (AT)    │           │
│  └─────────┘ └─────────┘ └─────────┘           │
└─────────────────────────────────────────────────┘
```

**MoA Configuration:**

```markdown
## Proposer Configuration

### Proposer 1: Optimization Focus (ToT)
- Objective: Find optimal solution
- Evaluation: Score-based ranking
- Output: Single best path with confidence

### Proposer 2: Exploration Focus (BoT)
- Objective: Map solution space
- Evaluation: Coverage-based
- Output: Top 5 viable options

### Proposer 3: Analogy Focus (AT)
- Objective: Cross-domain insights
- Evaluation: Structural mapping quality
- Output: Transferred principles

## Aggregator Configuration

### Aggregation Method: Weighted Synthesis
- Weight by proposer confidence
- Identify common themes across proposers
- Flag disagreements for explicit resolution

### Conflict Resolution
- If proposers agree: Boost confidence +5%
- If 2/3 agree: Use majority, document minority
- If no agreement: Escalate to DR (Dialectical Reasoning)
```

**MoA for Multi-Perspective Analysis:**

```markdown
## Problem: "Choose database for new microservice"

### Proposer 1 (ToT): Score-optimized
→ PostgreSQL (Score: 87/100)
  - Best for ACID compliance
  - Strong query performance

### Proposer 2 (BoT): Option-mapped
→ Top 3: PostgreSQL (72%), MongoDB (68%), DynamoDB (65%)
  - PostgreSQL: Relational, ACID
  - MongoDB: Flexible schema
  - DynamoDB: Serverless scale

### Proposer 3 (AT): Analogy-based
→ Recommendation: PostgreSQL
  - Analogy: Banking systems use relational for audit trails
  - Our use case: Financial transactions need same guarantees

### Aggregator Synthesis
Agreement Level: FULL (3/3 on PostgreSQL)
Combined Confidence: max(87%, 72%, 75%) + 5% = 92%

Final Recommendation: PostgreSQL with high confidence
- Optimization confirms performance
- Exploration confirms no better alternatives
- Analogy confirms domain fit
```

---

### Patt