hierarchical-matching-systems

层级匹配系统

本技能为层级匹配系统提供严格的诊断和架构流程。请严格遵循检查清单——匹配错误往往隐藏在被跳过的步骤中。

快速参考

• 算法选择：参阅 references/decision-guide.md
• 算法详情：参阅 references/algorithms.md

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1. 问题分类检查清单

开始任何工作之前，先对问题进行分类。勾选所有适用项：

□ TWO-SIDED: Both sides have preferences (students↔schools, workers↔jobs)
□ ONE-SIDED: Only one side has preferences (tasks→workers, items→bins)
□ HIERARCHICAL: Entities exist at multiple levels (org→dept→team→person)
□ WEIGHTED: Matches have costs/scores to optimize
□ CONSTRAINED: Hard limits exist (capacity, exclusions, required pairings)
□ STABLE: Solution must resist defection (no blocking pairs)
□ OPTIMAL: Solution must minimize/maximize objective function
□ FUZZY: Entities may partially match (entity resolution, deduplication)

分类结果决定算法类别。架构设计请转到第 2 节，调试请转到第 3 节。

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2. 架构流程

设计新的匹配系统时，按顺序遵循以下阶段。

Phase 2.1：需求转换

将每项业务需求转换为形式化约束：

业务需求	约束类型	形式化表达
“每位学生分配一所学校”	容量	`
“学校有座位数量限制”	容量	`
“兄弟姐妹必须在一起”	耦合	school(s1) = school(s2) if siblings(s1,s2)
“学生 X 不能就读 Y”	排除	(X, Y) ∉ matches
“优先考虑居民”	偏好排序	rank(resident) < rank(non-resident)

检查清单：

□ List ALL business requirements
□ Classify each as: capacity | coupling | exclusion | ordering | soft preference
□ Identify conflicts between requirements (document tradeoffs)
□ Distinguish HARD constraints (must satisfy) from SOFT (optimize toward)
□ Validate translations with stakeholder examples

Phase 2.2：算法选择

使用 references/decision-guide.md 选择算法。请确认：

□ Algorithm handles all HARD constraints
□ Algorithm can optimize SOFT constraints (or document gaps)
□ Complexity acceptable for data size (see references/algorithms.md)
□ Stability requirements met (if two-sided)
□ Optimality requirements met (if weighted)

Phase 2.3：数据模型设计

定义实体、关系和偏好表示方式：

□ Entity schema for each side (attributes, identifiers)
□ Preference representation (ranked list | score matrix | pairwise comparisons)
□ Constraint encoding (how exclusions/couplings are stored)
□ Hierarchy representation (if multi-level: tree | DAG | adjacency list)
□ Tie-breaking rules (deterministic ordering for equal preferences)

Phase 2.4：接口契约

明确输入、输出和不变量：

输入契约：

□ Preference format and validation rules
□ Constraint format and validation rules
□ Required vs optional fields
□ How missing preferences are handled (reject | default rank | exclude)

输出契约：

□ Match format (pairs | assignment map | ranked list)
□ Unmatched entity handling (explicit list | null matches | error)
□ Match metadata (scores, stability proof, constraint satisfaction report)

不变量：

□ Determinism: same input → same output (document randomness if any)
□ Completeness: all entities matched OR explicitly unmatched
□ Validity: all matches satisfy hard constraints

Phase 2.5：测试策略

在实现前定义验证方式：

□ Unit tests for preference parsing and constraint validation
□ Property tests: stability, optimality, constraint satisfaction
□ Edge cases: empty inputs, single entity, all tied preferences
□ Regression tests from known-good examples
□ Performance benchmarks at target scale

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3. 调试流程

遇到任何匹配问题时，都按以下诊断顺序执行。不得跳过步骤。

Phase 3.1：症状分类

确定症状类别：

症状	类别	转到
输入相同，输出不同	不稳定性	3.2
匹配违反业务规则	约束违反	3.3
匹配在技术上有效，但“错误”	偏好不一致	3.4
嵌套／层级数据出错	层级错误	3.5
规模扩大后性能不佳	性能	3.6

Phase 3.2：不稳定性诊断

非确定性匹配的根本原因：

□ RANDOMNESS: Check for unseeded RNG in tie-breaking
   → Fix: Use deterministic tie-breaker (lexicographic ID, timestamp)

□ FLOATING POINT: Check score comparisons for floating point issues
   → Fix: Use epsilon comparison or integer scores

□ HASH ORDERING: Check if iteration order depends on hash maps
   → Fix: Sort keys before iteration

□ PARALLEL RACE: Check for concurrent modifications
   → Fix: Synchronize or use sequential processing

□ INPUT ORDERING: Check if algorithm is order-sensitive
   → Fix: Canonicalize input order (sort by ID)

验证：

□ Run matching 10x with identical inputs
□ Diff all outputs
□ If any differ, add logging to identify divergence point

Phase 3.3：约束违反诊断

诊断顺序：

1. □ IDENTIFY: Which specific constraint is violated?
   → List the violated constraint and the violating match

2. □ TRACE: Where should constraint be enforced?
   → Map constraint to code location (filter | validation | algorithm step)

3. □ VERIFY ENCODING: Is constraint correctly represented?
   → Print constraint data structure, verify against requirement

4. □ VERIFY ENFORCEMENT: Is constraint checked at right time?
   → Add logging before/after enforcement point

5. □ CHECK ORDERING: Is constraint checked before conflicting decisions?
   → Trace decision sequence, verify constraint checked first

6. □ CHECK COMPLETENESS: Are all instances covered?
   → Enumerate all entities that should be constrained

常见失败模式：

模式	症状	修复方法
后期执行约束	中间状态有效，最终状态无效	提前执行检查
覆盖不完整	部分实体受约束，其他实体不受约束	列举所有情况
混淆软约束与硬约束	为了“更好”的匹配而违反约束	将其重新归类为硬约束
数据过时	约束基于过时的值	检查前刷新数据

Phase 3.4：偏好不一致诊断

当匹配有效但未体现预期优先级时：

1. □ EXTRACT: Get the actual preference data used
   → Log/print the exact preference structure at match time

2. □ COMPARE: Check against expected preferences
   → Side-by-side diff with business-stated priorities

3. □ TRACE TRANSFORMATION: Follow preference from input to algorithm
   → Log at each transformation step (parsing, normalization, scoring)

4. □ CHECK SCORING: Verify score calculation
   → Manual calculation for 2-3 example cases

5. □ CHECK AGGREGATION: If multi-criteria, verify combination
   → Test each criterion independently, then combined

6. □ CHECK NORMALIZATION: Verify scale/range handling
   → Check for min/max, z-score, or rank normalization bugs

评分函数检查清单：

□ Direction correct (higher = better or lower = better, consistently)
□ Scale appropriate (no single factor dominating)
□ Missing values handled (null → 0? → excluded? → default?)
□ Ties handled explicitly (not left to floating point chance)
□ Edge cases: extreme values, all same values, single candidate

Phase 3.5：层级遍历诊断

针对多层级匹配问题：

1. □ VISUALIZE: Draw the hierarchy with the problematic match
   → Tree diagram showing all levels and the match path

2. □ CHECK INHERITANCE: Do child constraints inherit from parent?
   → Verify constraint propagation rules

3. □ CHECK AGGREGATION: How do child preferences roll up?
   → Verify aggregation function (sum | max | weighted | majority)

4. □ CHECK LEVEL INTERACTION: Can matches cross levels?
   → Document allowed/forbidden cross-level matches

5. □ CHECK TRAVERSAL ORDER: Top-down or bottom-up?
   → Verify algorithm processes levels in intended order

6. □ CHECK PARTIAL MATCHES: Can a parent match without all children?
   → Document completeness requirements per level

常见层级错误：

错误	症状	修复方法
传播缺失	子级忽略父级约束	添加继承逻辑
重复计数	同一实体被多次加权	在汇总时去重
跳过层级	在错误的层级进行匹配	添加层级验证
孤立节点处理	未关联的子级导致错误	定义孤立节点策略

Phase 3.6：性能诊断

针对规模和速度问题：

1. □ PROFILE: Identify the slow component
   → Time each phase: input parsing, preference building, matching, output

2. □ COMPLEXITY CHECK: Verify actual vs expected complexity
   → Log iteration counts, compare to theoretical O(n)

3. □ MEMORY CHECK: Profile memory usage
   → Watch for preference matrix explosion (n² space)

4. □ ALGORITHM FIT: Verify algorithm appropriate for scale
   → See references/algorithms.md for complexity comparison

5. □ CACHING: Check for redundant computation
   → Log cache hits/misses for preference lookups

6. □ BATCH VS STREAMING: Check processing model
   → Full recomputation vs incremental updates

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4. 测试与验证流程

4.1：正确性属性

对每个匹配系统测试以下属性：

□ DETERMINISM: run(input) = run(input) (10 trials minimum)
□ COMPLETENESS: all entities either matched or explicitly unmatched
□ VALIDITY: all matches satisfy all hard constraints
□ STABILITY (if applicable): no blocking pairs exist
□ OPTIMALITY (if applicable): objective function at expected value

4.2：稳定性验证（双边匹配）

对于稳定匹配，验证不存在阻塞对：

# Pseudocode - verify no blocking pair exists
for each unmatched_pair (a, b):
    if a prefers b over current_match(a):
        if b prefers a over current_match(b):
            FAIL: blocking pair found (a, b)

□ Enumerate all non-matched pairs
□ Check mutual preference for each
□ Report any blocking pairs found
□ For large instances, sample-check (document coverage)

4.3：约束满足验证

□ List all hard constraints
□ For each match, verify against each constraint
□ Generate constraint satisfaction report
□ Flag any violations with specific match and constraint

4.4：边界情况测试套件

必测用例：

□ Empty input (no entities on one or both sides)
□ Single entity (one-to-one degenerate case)
□ All identical preferences (maximum tie scenario)
□ Mutually exclusive preferences (everyone wants same thing)
□ Impossible constraints (unsatisfiable, should error clearly)
□ Maximum capacity (all slots exactly filled)
□ Minimum capacity (barely enough slots)
□ Self-referential (can entity match itself? test boundary)
□ Circular preferences (A→B→C→A)

4.5：回归测试维护

□ Capture real production cases that revealed bugs
□ Minimize to smallest reproducing example
□ Document expected behavior explicitly
□ Run on every change to matching logic

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5. 审查清单

审查匹配系统代码或设计时：

5.1：设计审查

□ Problem correctly classified (Section 1)
□ Algorithm appropriate for problem class (references/decision-guide.md)
□ All business requirements mapped to constraints (Section 2.1)
□ Hard vs soft constraints clearly distinguished
□ Tie-breaking is deterministic and documented
□ Hierarchy semantics defined (if applicable)

5.2：实现审查

□ Preference representation matches algorithm requirements
□ Constraints enforced at correct point in algorithm
□ No hidden randomness (unseeded RNG, hash iteration)
□ Floating point comparison handled correctly
□ Edge cases handled (empty, single, ties)
□ Error messages identify specific constraint violations

5.3：测试审查

□ All properties from 4.1 tested
□ Edge cases from 4.4 covered
□ Performance benchmarked at realistic scale
□ Regression tests exist for past bugs

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附录：常见反模式

反模式	问题	解决方案
先到先得的贪心策略	依赖顺序，结果非最优	使用合适的算法
分数 = 所有因素之和	某一因素占主导	统一量纲
重试直到有效	结果不确定，速度慢	调整约束顺序
全局偏好缓存	更新后数据过时	发生变化时使缓存失效
用字符串匹配实体	大小写／空格导致错误	使用规范 ID
用浮点数判断相等以处理平局	结果不确定	使用 epsilon 或整数
递归遍历层级结构	存在栈溢出风险	使用带显式栈的迭代方式
N² 偏好矩阵	内存占用激增	使用稀疏表示