Getting it into your agent
One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.
npx skills add hajibabaie/combinatorial-optimization-skills --skill assignment-problemsgit clone --depth 1 https://github.com/hajibabaie/combinatorial-optimization-skillsWrote this? Show the measurements
A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.
[](https://agentmods.dev/skills/hajibabaie/combinatorial-optimization-skills/assignment-problems)<a href="https://agentmods.dev/skills/hajibabaie/combinatorial-optimization-skills/assignment-problems"><img src="https://agentmods.dev/badge/skills/hajibabaie/combinatorial-optimization-skills/assignment-problems/github.svg" alt="Measured on agentmods" height="20"></a>Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.
<a href="https://agentmods.dev/skills/hajibabaie/combinatorial-optimization-skills/assignment-problems"><img src="https://agentmods.dev/badge/skills/hajibabaie/combinatorial-optimization-skills/assignment-problems.svg" alt="Reviewed on agentmods" width="80" height="20"></a>What it costs to keep this loaded
Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5.1 | $0.00127 | $0.10532 |
| Opus 5.5 | $0.00051 | $0.04213 |
| Sonnet 5.5 | $0.00025 | $0.02106 |
| Haiku 4.5 | $0.00013 | $0.01053 |
Grade A, and why
assignment-problems scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 1mo ago.
A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.
Nothing flagged
None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.
How it starts
The opening of the file, as written. The whole thing — 900 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Assignment Problems
You are an expert in assignment problems: linear assignment (LAP), generalized assignment (GAP), and bottleneck assignment. This skill covers exact methods (Hungarian algorithm, LP with total unimodularity, MIP), Lagrangian bounds, and local-search heuristics, plus instance generation and independent solution validation. Use the framework below to classify the variant, pick the cheapest adequate method, implement it, and verify the result.
Initial Assessment
Establish these points before formulating or recommending a method:
- Cardinality structure. One agent per task and one task per agent (one-to-one, LAP)? Or can one agent take several tasks subject to a capacity (many-to-one, GAP)? This single distinction separates a polynomial problem from an NP-hard one.
- Objective sense and shape. Minimize total cost, maximize total profit, or minimize the worst single cost (bottleneck)? Mixed conventions are the most common source of wrong answers; fix the sense first.
- Sizes. Number of agents m, tasks n. LAP with n up to ~10,000 is
routine for
scipy.optimize.linear_sum_assignment. GAP with m·n up to ~10^5 binaries is usually fine for a MIP solver; beyond that plan for Lagrangian bounds plus a heuristic. - Balanced or rectangular. Equal numbers on both sides? If not, decide whether unmatched rows/columns are allowed and what they cost.
- Forbidden pairs. Are some (agent, task) combinations disallowed? Plan
to encode them as
np.inf(scipy) or by omitting variables (MIP), not as fragile big-M costs. - Resource data type (GAP). Integer resource consumptions enable knapsack DP in the Lagrangian subproblems; float data must be scaled or the subproblems solved as small MIPs.
- Solve count. One-off solve, or LAP/GAP called thousands of times inside a heuristic or branch-and-bound loop? The embedded case changes the tooling (warm starts, C-backed LAP libraries, candidate lists).
- Solver availability. Gurobi license present? If not, scipy + open-source MIP (HiGHS) covers everything in this skill.
- Optimality requirement. LAP and bottleneck are always exact. For GAP, ask whether a proven optimum is required or a bounded-gap heuristic solution within a time budget suffices.
- Validation path. Agree up front that every reported solution passes an independent feasibility and objective check (provided below).
What this file has done since we first saw it
Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.
- 1mo ago First seen · 900 lines · 127 tokens per session scan A 0b3a5fbcb13b
assignment-problems is a skill published in the GitHub repository hajibabaie/combinatorial-optimization-skills (14 stars, last pushed 4mo ago), licensed MIT. It adds 127 tokens to every session and 10,532 once invoked, about $0.0005 per session on Opus 5.5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-08-31.
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