{"schema_version":"1.0","canonical_url":"https://patentable.app/patents/US-8493411","patent":{"patent_number":"US-8493411","title":"Methods and apparatus for extensions to directed graphs with minimal and maximal constraints are encoded by arcs in opposite directions","assignee":null,"inventors":[],"filing_date":"2012-08-03T00:00:00.000Z","publication_date":"2013-07-23T00:00:00.000Z","cpc_codes":["G06F"],"num_claims":30,"abstract":"Disclosed are apparatus and methods for generating displays based on a layout. A layout is received that specifies a set of rectangular components within a container rectangle. Each rectangular component has a size. A plurality of grid lines is determined from the layout. Each rectangular component is associated with at least two grid lines that are based on the size of the rectangular component. A system of constraints is generated that includes a minimum constraint and a maximum constraint. Each constraint is related to at least two grid lines of the plurality of grid lines. The minimum and maximum constraints respectively specify a minimum and a maximum value between at least two grid lines. The system of constraints is solved to determine a location for each grid line. A display of the rectangular components is generated based on the locations of the grid lines."},"analysis":{"summary":null,"layman_explanation":null,"technical_analysis":null,"business_analysis":null,"faqs":null,"topics":[],"tech_cluster":null},"seo":{"title":"Methods and apparatus for extensions to directed graphs with minimal and maximal constraints are encoded by arcs in opposite directions","description":"Disclosed are apparatus and methods for generating displays based on a layout. A layout is received that specifies a set of rectangular components within a container rectangle. Each rectangular compon","keywords":[]},"attribution":{"source":"Patentable","source_url":"https://patentable.app","canonical_url":"https://patentable.app/patents/US-8493411","license":"CC-BY-4.0-like","license_terms":"AI-generated analysis on this page (summary, layman_explanation, technical_analysis, business_analysis, faqs) may be reused with attribution and a visible link back to the canonical URL above. Patent abstracts, claims, and bibliographic data are USPTO public domain.","required_link":"https://patentable.app/patents/US-8493411","citation_suggestion":"Patentable. \"Methods and apparatus for extensions to directed graphs with minimal and maximal constraints are encoded by arcs in opposite directions\" (US-8493411). https://patentable.app/patents/US-8493411","copyright_holder":"Nomic Interactive Technology LLC"},"links":{"html":"https://patentable.app/patents/US-8493411","json":"https://patentable.app/api/llm-context/US-8493411","site":"https://patentable.app","llms_txt":"https://patentable.app/llms.txt"},"generated_at":"2026-05-30T13:23:37.560Z"}