Quick wins for a faster PC:
Clear out junk files and repair common Windows errorsFree Scan →Fix the driver behind crashes, sound loss and screen glitchesFind Drivers →Use a linear assignment solver for one-to-one matching with pairwise costs; use min-cost flow when capacities, supplies and demands, or a broader network are part of the problem. Assignment can also be modeled as min-cost flow, so the practical choice is usually the formulation that matches your constraints and the solver API—not a claim that one method is always faster.
Start with the shape of the constraints
Ask whether you are pairing items from two groups, or routing units through a network.
- Pairing: Each selected worker–job or item–task pair has a cost, and each item can be used at most once. This is the linear assignment problem.
- Routing: Nodes provide or require quantities, and directed arcs have capacities and costs. This is the broader min-cost flow model.
A standard assignment can be represented as a flow network: connect a source to workers, workers to eligible tasks, and tasks to a sink; give assignment arcs their pair costs. OR-Tools documents this reduction in its assignment-as-minimum-cost-flow example. If the problem has no meaningful network constraints beyond the one-to-one pairing, a direct assignment API is usually the clearer expression.
How the models differ
| Question | Linear assignment | Min-cost flow |
|---|---|---|
| What is being optimized? | Total cost of selected pairs, with each row and column used at most once. See SciPy’s assignment API. | Total cost of sending flow through a directed graph subject to node demands and edge capacities. See NetworkX’s min-cost-flow API. |
| Natural input | A dense row-by-column cost matrix, or a sparse bipartite graph if the solver provides that API. | A graph whose nodes have supplies or demands and whose arcs have costs and capacities. |
| When it fits best | One-to-one allocation without additional network requirements. | Multiple units per entity, capacity limits, or conservation of supply and demand across a network. |
| Unmatched items | Depends on the API and matrix shape; confirm its cardinality convention against your policy. | Depends on the specified supplies, demands, capacities, and feasibility of the network. |
Choose based on your actual use case
Use linear assignment for a pairwise allocation
Choose assignment when each worker can take at most one job and each job can go to at most one worker, with a cost for each allowed pairing. SciPy’s linear_sum_assignment accepts rectangular matrices; when the two sides differ in size, not every row or column must be assigned. Its documented objective is to minimize the total cost of selected row-column pairs. The current development documentation describes a modified Jonker–Volgenant implementation, but implementation details can vary by release, so consult the documentation for the SciPy version you deploy.
Do these 3 things before closing this tab:
1Clear out junk files and repair common Windows errors2Scan for outdated or missing drivers - takes under a minute3Repair Windows errors before they cause bigger problems#1 Best Overall
- Read Before You Buy — No Video Output: These adapters support charging and USB 2.0 data transfer, but cannot transmit video signals. Except for standard USB webcams (which use USB data only), they are not compatible with HDMI/DisplayPort cables, video-capable USB-C hubs, or docking stations with video output.
- Convert USB-A Ports to USB-C: Designed to connect USB-C earphones, cables, flash drives, card readers, and other USB-C accessories to standard USB-A ports. Plug-and-play with no drivers or software required.
- Aluminum Alloy Housing: Built with a sturdy aluminum alloy shell that aids in heat dissipation and protects against daily wear and scratches. Designed to maintain a stable and secure connection.
- Compact & Travel-Friendly: The ultra-compact design allows the adapter to stay plugged into your device without blocking adjacent ports or adding bulk, reducing wear and tear on your original USB ports.
- 12-Month Warranty: Backed by a 12-month manufacturer warranty for peace of mind. Designed to meet strict quality control standards for reliable everyday performance.
Google OR-Tools also documents a separate linear sum assignment solver. A dedicated API keeps the model close to the problem statement and avoids adding flow machinery that is not needed.
Use min-cost flow when quantities or routes matter
Choose min-cost flow when an entity can supply or receive multiple units, when links have capacities, or when the problem requires quantities to move through a network while respecting node supply and demand. These are native parts of the flow model, rather than details you have to approximate as individual one-to-one pairs.
Rank #2
- 5-in-1 USB-C Hub: Experience comprehensive connectivity featuring a Power Delivery input, two USB-A 2.0 ports, a USB-A 3.0 port, and an HDMI port. (Note: The USB-C power delivery input port is only for connecting an external wall charger to power your laptop and cannot power peripheral devices.)
- 90W Pass-Through Charging: Achieve optimal charging with 90W pass-through power to your laptop, supported by a total input of 100W, with the hub reserving 10W for operational efficiency. (Note: Wall charger not included.)
- Quick Data Transfers: Accelerate your productivity with rapid data transfers using a high-speed 5Gbps USB 3.0 port and two 480Mbps USB 2.0 ports.
- 4K HDMI Display: Enhance your visual experience with a hub capable of delivering 4K resolution at 30Hz in both mirror and extend modes. Please note that this hub is compatible with MacBook (macOS 12 and newer), Windows 10 and 11, ChromeOS, and laptops equipped with DP Alt Mode and Power Delivery. Note: This device is not compatible with Linux.
- What You Get: Anker USB-C Hub (5-in-1, 4K HDMI), welcome guide, 18-month warranty, and our friendly customer service.
For NetworkX specifically, min_cost_flow works with node demands and edge capacities and costs. Its documentation requires total node demand to sum to zero for feasibility, and warns that its implementation is not guaranteed for floating-point edge weights or demands because of roundoff and overflow. Treat that as a NetworkX-specific limitation, not a general statement about every min-cost-flow solver.
Do not assume every side constraint is a flow constraint
Assignment plus capacities or network conservation can often be modeled naturally as flow. But arbitrary extra rules do not automatically fit ordinary min-cost flow. If a constraint cannot be expressed through the network’s arcs, capacities, supplies, and demands, check whether the chosen solver supports it or whether a different optimization model is needed.
Rank #3
- Sleek 7-in-1 USB-C Hub: Features an HDMI port, two USB-A 3.0 ports, and a USB-C data port, each providing 5Gbps transfer speeds. It also includes a USB-C PD input port for charging up to 100W and dual SD and TF card slots, all in a compact design.
- Flawless 4K@60Hz Video with HDMI: Delivers exceptional clarity and smoothness with its 4K@60Hz HDMI port, making it ideal for high-definition presentations and entertainment. (Note: Only the HDMI port supports video projection; the USB-C port is for data transfer only.)
- Double Up on Efficiency: The two USB-A 3.0 ports and a USB-C port support a fast 5Gbps data rate, significantly boosting your transfer speeds and improving productivity.
- Fast and Reliable 85W Charging: Offers high-capacity, speedy charging for laptops up to 85W, so you spend less time tethered to an outlet and more time being productive.
- What You Get: Anker USB-C Hub (7-in-1), welcome guide, 18-month warranty, and our friendly customer service.
Handle sparse eligibility and unmatched items explicitly
When only some pairs are allowed
If most worker–task combinations are forbidden, a dense matrix may be an awkward representation. SciPy provides min_weight_full_bipartite_matching for sparse bipartite graphs. It seeks a matching with cardinality equal to the smaller partition and raises an error if that full matching cannot be found. NetworkX’s minimum_weight_full_matching offers the same rectangular full-assignment interpretation and delegates the calculation to SciPy. See the SciPy sparse matching documentation and NetworkX’s full matching documentation.
When some items may remain unmatched
“At most once” does not by itself say how many matches the application requires. Decide whether the goal is a perfect matching, a full matching of the smaller side, or a smaller number of assignments that reflects the business rules. Rectangular assignment APIs may leave items on the larger side unassigned; a sparse full-matching API may instead fail if it cannot match every vertex in the smaller partition. If you need a different policy, encode that policy deliberately and verify the solver’s behavior rather than relying on a default.
Rank #4
- Dual Converters, Infinite Potential：Includes 2× USB C male to USB A female adapters and 2× USB A male to USB C female adapters. Perfect for a wide range of uses—tablets with Bluetooth keyboards, expand USB ports on macbook, and more. Two different converters for all your daily needs
- Next-Level 10Gbps & 3A Charging: No more slow 480Mbps, this usb to usb c adapter has a transfer speed of up to 10Gbps, allowing you to do more transferring in less time. This usb adapter fits both USB A and USB C charger, supporting up to 3A fast charging
- Upgraded Exquisite Craftsmanship: With an aluminum alloy housing and metal connector, the usbc to usb adapter is extremely durable and sturdy. Rigorously tested to withstand more than 10,000 times of plugging and unplugging, ensuring long-lasting performance
- Broad Compatible: The usb c to usb adapter widely supports all USB C/ USB A devices like laptops, tablets, cellphones, car chargers, and phone chargers. Such as compatible with MacBook Pro/Air 2023/2022, Thunderbolt 4/3 Devices,Apple MagSafe Watch 9/8/7/SE/Ultra, iPad Pro 2022/2021, Samsung Galaxy S23/S20/S10, and iPhone 17/16/15 Pro. Plug and play
- Please Note: To reach 10Gbps speed, keep the cable under 3.3 ft. For USB A Male to USB C adapters, try flipping the USB C connector. USB C Male to USB A adapters support bidirectional 10Gbps transfer within 3.3 ft
Check solver and numeric behavior before implementation
- Input type: Determine whether your data is best represented as a dense matrix or a sparse allowed-edge graph, and use an API designed for that representation.
- Cardinality: Confirm exactly which items must be matched and what happens when no feasible full matching exists.
- Numeric support: Check the documentation for your chosen library’s handling of costs and demands. NetworkX’s floating-point warning applies to its min-cost-flow implementation; it should not be generalized to other libraries.
- Version: Solver algorithms and API behavior are version-specific. Check the documentation for the version installed in production.
- Performance: No universal runtime winner is established by the cited documentation. If speed matters, benchmark equivalent formulations using representative inputs, the intended library version, and the numeric types you will actually use.
A practical decision checklist
- Write down the entities and rules. If the rule is “each item gets at most one partner,” start with linear assignment. If units travel through capacity-limited links, start with min-cost flow.
- Specify the matching requirement. State whether the solution must match both sides, the smaller side, or only a chosen number of items.
- Choose the representation. Use a cost matrix for dense pairwise costs; use a sparse matching API when only a subset of pairs is allowed. Use a network for supplies, demands, and arc capacities.
- Verify the library’s semantics. Check the exact API’s cardinality, infeasibility behavior, and numeric caveats in the documentation for your version.
- Benchmark only if performance is decisive. Compare equivalent models on representative cases instead of assuming one formulation is faster.
Bottom line
For plain one-to-one matching, use a linear assignment solver. For capacity-constrained movement through a network, use min-cost flow. When assignment is only one part of a larger network, flow may be the more natural representation; choose based on the constraints you must express and the behavior of the specific solver you plan to use.
Quick Recap
Best Value
- 5-in-1 Connectivity: Equipped with a 4K HDMI port, a 5 Gbps USB-C data port, two 5 Gbps USB-A ports, and a USB C 100W PD-IN port. Note: The USB C 100W PD-IN port supports only charging and does not support data transfer devices such as headphones or speakers.
- Powerful Pass-Through Charging: Supports up to 85W pass-through charging so you can power up your laptop while you use the hub. Note: Pass-through charging requires a charger (not included). Note: To achieve full power for iPad, we recommend using a 45W wall charger.
- Transfer Files in Seconds: Move files to and from your laptop at speeds of up to 5 Gbps via the USB-C and USB-A data ports. Note: The USB C 5Gbps Data port does not support video output.
- HD Display: Connect to the HDMI port to stream or mirror content to an external monitor in resolutions of up to 4K@30Hz. Note: The USB-C ports do not support video output.
- What You Get: Anker 332 USB-C Hub (5-in-1), welcome guide, our worry-free 18-month warranty, and friendly customer service.
Product prices and availability are accurate as of the date/time indicated and are subject to change. Any price and availability information displayed on Amazon at the time of purchase will apply.
What’s actually slowing this PC down?
Pick the symptom - the matching free tool is one click away.
