maximum-flow

A guide to maximum-flow problems, where material or assignments move through a network with limits on each connection from a source to a destination.

In plain words
What is it for?
Modeling transport, assignments, disjoint paths, escape routes, image-segmentation cuts, and bipartite matching reductions.
Why use it?
It helps build a correct network model and verify the answer with residual paths and a cut that proves no larger flow is possible.

Skill for Claude CodeCodex

Install

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.

agentmods
npx agentmods add skills/arcadi4/nerdy/maximum-flow
Any agent
npx skills add Arcadi4/nerdy --skill maximum-flow
Clone the repo
git clone --depth 1 https://github.com/Arcadi4/nerdy

Made for: Claude Code, Codex.

Per session 59 Skills are progressive disclosure: only the name and description are preloaded; the body loads when the skill is used.
When invoked 3,824 The whole file, excluding the scripts and references it only reads on demand.
Security scan A 0 findings. Scan, not verified.
Origin original No closer match found in the catalogue.
Token cost

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.

ModelPer sessionOnce invoked
Fable 5 $0.00059 $0.03824
Opus 5 $0.00030 $0.01912
Sonnet 5 $0.00012 $0.00765
Haiku 4.5 $0.00006 $0.00382

Measured 2d ago against content hash e2f4713172a2, method: parsed. Prices are Anthropic first-party input rates as of 2026-08-30, from the pricing page.

Security

Grade A, and why

maximum-flow 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 2d 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.

clrs/maximum-flow/SKILL.md · 298 lines

How it starts

The opening of the file, as written. The whole thing — 298 lines — stays where its author put it; the contents beside it link to each section on GitHub.

Maximum Flow

Overview

Use this skill to decide whether a problem is really a flow model, a cut certificate, an augmenting-path algorithm question, or a matching reduction before naming an algorithm.

Core principle: a maximum-flow answer is correct only when the model preserves capacity constraints, conservation, residual cancellation, and the cut certificate that proves optimality.

Shared CLRS Conventions

  • Follow the parent clrs skill for mathematical formatting: every formula, inequality, asymptotic bound, and symbolic expression belongs in a display LaTeX block.
  • Use chapter-specific theorem names here, and keep shared graph traversal mechanics in elementary-graph-algorithms.
  • State the graph direction, source and sink convention, capacity domain, and whether integrality matters before using Ford-Fulkerson, Edmonds-Karp, or a matching reduction.
  • Keep tables verbal. Put capacities, residual definitions, and running times in display blocks near the table instead of inside table cells.

When to Use

Use this skill when a task involves:

  • modeling transport, assignment, disjoint paths, escape routes, image segmentation-style cuts, or feasibility through capacities;
  • proving a flow is maximum or extracting a minimum cut from a residual network;
  • choosing or analyzing Ford-Fulkerson, Edmonds-Karp, capacity scaling, or push-relabel-style production alternatives;
  • reducing bipartite matching, vertex capacities, multiple sources, multiple sinks, or antiparallel directed edges to ordinary single-source single-sink flow;
  • reviewing an implementation that maintains residual edges, reverse edges, bottlenecks, or integer-flow assumptions.

Do not use this skill merely because a graph is directed. If the task is shortest paths, reachability, strongly connected components, spanning trees, or topological order without capacities and conservation, route to elementary-graph-algorithms, shortest-paths, or minimun-spanning-trees as appropriate instead.

Read the full file on GitHub · 298 lines

Changes

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.

  1. 2d ago First seen · 298 lines · 59 tokens per session scan A e2f4713172a2

Subscribe to this mod's changes

maximum-flow is a skill published in the GitHub repository Arcadi4/nerdy (7 stars, last pushed 4mo ago), licensed MIT. It adds 59 tokens to every session and 3,824 once invoked, about $0.0003 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.

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