Arxiv Research

Purpose

Bridge gap between classical textbooks (TAOCP, CLRS) and cutting-edge academic research. Find modern approaches, recent optimizations, and alternative solutions published after canonical references.

When to Use

• After algorithmic_analysis Phase B completes
• Have candidate algorithms from textbooks
• Need to validate: "Is there newer work we're missing?"
• Before Stage 3 (design selection) to ensure comprehensive candidate set

Methodology

Input: List of candidate algorithms from algorithmic_analysis Output: Recent papers, modern variants, performance improvements, alternative approaches

Instructions

1. Extract Search Keywords

From problem specification and candidate algorithms, identify:

• Problem domain: Core problem name (e.g., "merge sorted sequences", "dynamic connectivity")
• Key operations: What operations are critical? (e.g., "priority queue", "incremental update")
• Constraints: What makes this hard? (e.g., "cache-oblivious", "external memory", "parallel")
• Classical solutions: Names from textbooks to search variants of

2. Systematic Arxiv Search

CRITICAL: Use WebSearch with arxiv-specific queries

Search Strategy (execute all, don't stop early):

a. Recent surveys:

• "arxiv [problem domain] survey"
• "arxiv [problem domain] algorithms recent"

b. Optimization papers:

• "arxiv [classical algorithm name] optimization"
• "arxiv cache-aware [problem domain]"
• "arxiv cache-oblivious [problem domain]"

c. Modern hardware adaptations:

• "arxiv SIMD [problem domain]"
• "arxiv GPU [problem domain]"
• "arxiv multicore [problem domain]"

d. Theoretical improvements:

• "arxiv [problem domain] lower bound"
• "arxiv optimal [problem domain]"
• "arxiv [problem] complexity"

e. Related problem space:

• "arxiv [related problem] algorithm"
• Search for problems that share data structures/techniques

3. Extract Information

For each relevant paper found:

PAPER: [Title]
AUTHORS: [Names]
YEAR: [Year]
ARXIV: [arxiv.org/abs/XXXX.XXXXX]

RELEVANCE:
- Addresses same problem? Yes/No/Related
- New algorithm? Name: [...]
- Optimization of existing? Which: [...]
- Theoretical result? What: [...]

KEY CONTRIBUTION:
- [1-2 sentence summary]

COMPLEXITY:
- Time: [...]
- Space: [...]
- Compared to classical: [improvement/different trade-off]

SHOULD WE ANALYZE?
- Yes (new candidate) / Maybe (optimization) / No (different problem)
- Reason: [...]

4. Categorize Findings

New Candidates: Full algorithms not in textbooks

• Add to candidate list for analysis

Optimizations: Improvements to existing algorithms

• Note for comparative_complexity stage

Theoretical Results: Lower bounds, impossibility

• Check against Phase A lower bound analysis

Related Work: Different problem, but relevant techniques

• Document for future reference

Dead Ends: Not applicable

• Brief note why (avoid re-searching later)

5. Output Format

Create summary document (e.g., 02-analysis/arxiv-survey.md):

# Modern Literature Survey

## Search Date
[YYYY-MM-DD]

## Keywords Searched
- [keyword 1]
- [keyword 2]
...

## New Candidates Found

### [Algorithm Name]
- **Paper**: [Authors, Year, arxiv link]
- **Contribution**: [summary]
- **Complexity**: Time O(...), Space O(...)
- **Status**: Should add to candidate-algorithms.tex as CANDIDATE N
- **Notes**: [any caveats, assumptions, trade-offs]

## Optimizations of Existing Candidates

### Optimization: [name]
- **Improves**: [which classical algorithm]
- **Paper**: [citation]
- **Technique**: [what's different]
- **Benefit**: [theoretical or empirical]
- **Status**: Defer to Stage 3 or mention in Stage 7 report

## Theoretical Results

### [Result]
- **Paper**: [citation]
- **Finding**: [new lower bound / impossibility / etc.]
- **Impact**: [does it change our analysis?]

## Related Work (Different Problem)

### [Topic]
- **Papers**: [list]
- **Relevance**: [why it might matter later]

## Search Dead Ends

- Query "[...]" → No relevant results
- Query "[...]" → All older than TAOCP/CLRS
- Query "[...]" → Different problem domain (not applicable)

## Recommendations

**Add to Analysis**:
1. [Algorithm X] - new candidate, should analyze
2. [Algorithm Y] - variant worth comparing

**Defer to Later Stages**:
1. [Optimization Z] - mention in Stage 3 comparative analysis
2. [Paper W] - cite in Stage 7 related work

**Archive for Future**:
- [Topic] - interesting but out of scope

Integration with Pipeline

Input from: algorithmic_analysis (Phase B candidate list)

Output to:

• algorithmic_analysis: Add new candidates if found
• comparative_complexity: Note optimizations for comparison
• technical_exposition: Cite in related work section

Timing: Execute AFTER Phase B initial analysis, BEFORE finalizing candidate list

Quality Checks

• Searched at least 5 different query formulations
• Checked papers from last 10 years minimum
• Extracted arxiv links for all relevant papers
• Categorized each finding (candidate/optimization/related/dead-end)
• Made explicit recommendation: analyze now vs defer vs ignore

Notes

Modern Focus: This skill complements textbook research, doesn't replace it

• TAOCP/CLRS: Classical, proven, foundational
• Arxiv: Recent, experimental, cutting-edge

Trade-offs:

• Newer doesn't mean better (maturity matters)
• Arxiv papers vary in quality (not peer-reviewed yet)
• Cite with appropriate caveats

When to Skip:

• Problem is purely classical (sorting primitives, basic search)
• Textbook analysis already exhaustive
• Time constraints (can mention limitation in report)

Cross-Skill Integration

Requires:

• problem_specification: Need problem definition to generate queries
• algorithmic_analysis Phase B: Need baseline candidate list

Feeds into:

• algorithmic_analysis: May add candidates
• comparative_complexity: Modern optimizations to compare
• technical_exposition: Related work citations