Min-Cost Flow Item Recommendations via Graph Optimization
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Solution Overview
Problem
Existing item recommendation approaches often result in sub-optimal solutions due to ignoring eligibility constraints and enforcing strict or non-strict capacity constraints, leading to inefficiencies in optimizing the recommendation of items to accounts.
Innovation Solution
The use of a minimum cost flow algorithm to determine item allocation to accounts by formulating the constrained optimization problem as a min-cost flow problem, leveraging a directed graph with nodes representing accounts and items, and employing the network simplex algorithm for efficient linear programming solutions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If existing recommendation approaches rank items ignoring eligibility constraints, then the recommendation process is simple, but the solution becomes sub-optimal
Solution Approach 1:
The patent segments the recommendation problem into distinct components: item scoring/ranking, eligibility constraint validation, and capacity constraint enforcement. By separating these functions and processing them in a coordinated manner rather than sequentially filtering, the system achieves both computational efficiency and optimality. The segmentation allows each component to be optimized independently while ensuring global optimality through the integrated approach.
2Reliability
If strict capacity constraints are enforced downstream after optimization, then capacity limits are guaranteed, but the optimization becomes sub-optimal
Solution Approach 1:
The patent applies preliminary action by incorporating capacity constraints directly into the optimization model before solving, rather than enforcing them downstream after optimization. The system pre-processes capacity information and integrates it with eligibility constraints to formulate a comprehensive optimization problem that guarantees both optimality and constraint satisfaction in a single computational pass.
3Adaptability or versatility
If model does not strictly enforce capacity constraints (satisfying on average), then the optimization is more flexible, but the constraints are not reliably satisfied
Solution Approach 1:
The patent applies local quality by treating capacity constraints as local requirements specific to each item type rather than global averages. The optimization model incorporates item-specific capacity limits that must be satisfied individually for each item, allowing the system to maintain flexibility in overall allocation while ensuring reliable satisfaction of each specific capacity constraint through localized enforcement.
Data Source
AI summary
Techniques are provided for optimizing a graph. The graph can be generated with a source node, a plurality of item nodes, and a terminal node. Once generated, the graph can be optimized to determine a lowest cost flow from the source node to the terminal node based at least in part on respective budget measurements. A first account node and a first item node can be determined and an account corresponding to the first account node, as well as information that identifies an item corresponding to the first item node can be transmitted.