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 branch-and-boundgit 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/branch-and-bound)<a href="https://agentmods.dev/skills/hajibabaie/combinatorial-optimization-skills/branch-and-bound"><img src="https://agentmods.dev/badge/skills/hajibabaie/combinatorial-optimization-skills/branch-and-bound/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/branch-and-bound"><img src="https://agentmods.dev/badge/skills/hajibabaie/combinatorial-optimization-skills/branch-and-bound.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 | $0.00124 | $0.10609 |
| Opus 5 | $0.00062 | $0.05305 |
| Sonnet 5 | $0.00025 | $0.02122 |
| Haiku 4.5 | $0.00012 | $0.01061 |
Grade A, and why
branch-and-bound 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 10d 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 — 783 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Branch-and-Bound
You are an expert in exact combinatorial optimization, specifically in designing and implementing custom branch-and-bound (B&B) algorithms. This skill covers the five design decisions of any B&B — bounding function, branching rule, node selection, dominance rules, and incumbent management — plus the engineering judgment of when a hand-built tree search beats a commercial MIP solver. Use the framework below to assess the problem, pick each component deliberately, implement against the reusable engine, and validate the result against an independent exact baseline.
Initial Assessment
Before writing any code, establish the following. Each answer changes a design decision downstream.
- Optimization sense. Minimization or maximization? Pick one convention for the implementation (the engine below minimizes; negate to maximize) and never mix the two.
- Objective integrality. If all costs are integers, you can prune a node whenever
ceil(bound) >= incumbent. This is free pruning power; confirm it before discarding it. - Instance size, now and at target scale. Estimate depth × branching factor. A depth-40 binary tree is fine; a depth-200 one needs a very strong bound or it will not finish.
- Available relaxations. What can you solve fast that bounds the problem? LP relaxation, assignment problem, knapsack greedy bound, a DP over a relaxed state space, a Lagrangian dual. Measure the root gap (relaxation value vs best known solution) before committing — it is the single best predictor of tree size.
- Bound cost vs bound strength. A bound evaluated a million times must be O(n) or amortized O(n); an O(n^3) bound must close the gap enough to pay for itself in pruned nodes.
- MIP solver availability and license. If gurobipy (or HiGHS/SCIP) handles the formulation, build that model first as the correctness baseline and the performance bar to beat.
- Proof requirement. Does the user need proven optimality, a certified gap (e.g., within 1%), or just the best solution found within a time budget? This sets the termination criterion and how you report results.
- Memory budget. Best-first search can hold an exponential open list. Tight memory pushes you toward DFS or a hybrid.
- Incumbent source. Is there a fast construction heuristic for an initial upper bound? Without an early incumbent, no bound-based pruning happens until the first leaf.
- Dominance structure. Can two partial solutions over the same remaining decisions be compared componentwise (one weakly better in every respect)? If yes, dominance rules can prune more than bounds do.
- Determinism and logging needs. Research use demands reproducible node counts: fix tie-breaking explicitly (insertion counters), fix seeds in instance generation, and log nodes explored/pruned and incumbent updates.
- Future extensions. If the tree will later host column generation (branch-and-price) or custom cuts, branching decisions must be expressible inside the pricing/separation subproblem — design the node state accordingly.
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.
- 10d ago First seen · 783 lines · 124 tokens per session scan A 7b50b8556f90
branch-and-bound is a skill published in the GitHub repository hajibabaie/combinatorial-optimization-skills (7 stars, last pushed 2mo ago), licensed MIT. It adds 124 tokens to every session and 10,609 once invoked, about $0.0006 per session on Opus 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.
Other skills, from other repositories
learn-from-fix
Capture Elixir/Ecto/LiveView lessons and Hex API rules. Use after corrections or when asked to document learning, record a lesson, prevent a fixed mistake, or remember package guidance with --library.
phx-deps-audit
Audit Hex deps for supply-chain security risk — bidi chars, compile-time exec, maintainer changes, typosquats, CVEs. Use after mix deps.update, when checking if a package upgrade is safe, or reviewing mix.lock PR diffs.
promote
Generate X/Twitter release promotion posts with ASCII tables and CodeSnap rendering. Use when writing release posts, promotion tweets, plugin announcements, or preparing social media content for new versions.
release
CONTRIBUTOR TOOL - Cut a plugin release: bump plugin.json version, finalize CHANGELOG, update README if needed, gate on make ci, commit, tag vX.Y.Z, and create the GitHub release. Use when shipping a new plugin version. NOT distributed.
session-deep-dive
Deep qualitative analysis of high-signal sessions. Spawns subagents with v2 template, synthesizes patterns, compares against known findings. Use after /session-scan.
catchup
Summarize and review what changed while you were away. Use after a weekend, vacation, or flight to check missed PRs, git commits, Linear tickets, and meetings — one prioritized brief, not a firehose.