Count linear extensions via OrderPolytope volume approximation with optimized HMC oracles#478
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ChinmayRout9040895625 wants to merge 2 commits intoGeomScale:developfrom
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- Add S4 class for Spectrahedron representation - Implement volume computation methods (CB, SOB) with 4 random walk types - Implement uniform sampling from spectrahedra with RDHR, CDHR, HMC, BILLIARD walks - Add Rcpp wrappers for volume and sampling computations - Add helper functions for SDPA file loading and spectrahedron creation - Add comprehensive test suites for volume and sampling - Add Roxygen2 documentation for Spectrahedron class and methods This implements the core functionality for GSOC 2026 proposal: Spectrahedra R interface for volesti package.
vissarion
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Thanks for this PR.
Could you give more information? What is the volume algorithm you are using and what is the performance gain and with which inputs?
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Implements a new approximation algorithm for counting linear extensions of partial orders
through volume estimation of order polytopes, using the identity #LE(P) = n! × Vol(OrderPolytope(P)).
(1) Changes
Optimized HMC Boundary Oracles (orderpolytope.h)
structure for O(d + num_relations) instead of O(d × m)
NOMINMAXand_USE_MATH_DEFINESguards(2) New Files
examples/count-linear-extensions/— CLI tool comparing OrderPolytope vs HPolytope, with CMake and sample poset data files