Graphs -> Flow With Lower Bounds¶

Feasible circulation and lower/upper edge bounds reduced to one saturating max-flow check with super source and super sink.

Microtopics¶

Source	Type
CP-Algorithms flows with demands	`Reference`
USACO Guide flow with lower bounds	`Reference`
Illinois CS473 flow extensions	`Course`

Source	Type
Codeforces acmsguru Reactor Cooling	`Practice`
Library Checker min_cost_b_flow	`Practice`
Codeforces problemset	`Practice`

Material	Type
Flow With Lower Bounds hot sheet	`quick reference`
Reactor Cooling note	`anchor note`
Flow starter route	`starter route`
Maximum Flow tutorial	`adjacent tutorial`
Min-Cost Flow tutorial	`compare point`

Problem	Source	Difficulty	Context	Style	Prerequisites	Tags	Why it fits
Reactor Cooling	`Codeforces acmsguru`	`Hard`	Lower Bounds	Reduction; Witness Output	Maximum Flow; Residual Graph; Super Source / Super Sink	Feasible Circulation; Balance Array; Witness Output	The canonical first lower-bounds circulation problem: every edge has mandatory minimum and maximum flow, and you must print one witness in input order.

Problem	Source	Difficulty	Context	Style	Prerequisites	Tags	Why it fits
Minimum Cost b-Flow	`Library Checker`	`Hard`	Lower Bounds, Cost	Verification; Cross-Topic	Flow With Lower Bounds; Min-Cost Flow; Supply / Demand Modeling	Node Supply/Demand; Costed Flow	A strong official compare point showing how lower bounds and node balances grow into the costed b-flow family.

Code	Title	Fit	Difficulty	Pattern	Note	Solution
`REACTORCOOLING`	Reactor Cooling	`secondary`	`hard`	feasible circulation; lower bounds; flow reconstruction	Note	Code

python3 scripts/generate_problem_catalog.py