Definable functions in FO(Z,+,≤), FO(R,+,≤) and FO(R,Z,+,≤) are exactly the piecewise-linear or piecewise-simple functions, and mixed sets coincide with semi-polinear sets.
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Thiele rules are polynomial-time computable on voter interval elections via a standard LP that always has an integral optimum, extending to VCI and LC domains with NP-hardness shown on tree-based generalizations.
Faster FPT algorithms for Telephone Broadcast achieve 2^{O(vc log vc)}, 2^{O(vi^2 log vi)}, and 2^{O(k log k)} n^{O(1)} time via reduction to b-Matching.
Optimal policies under budget and coverage constraints admit an affine threshold characterization with O(1) integrality gap in the LP relaxation; two algorithms (GLC and RC) are analyzed with performance guarantees that depend on cost homogeneity and constraint bindingness.
citing papers explorer
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Extending the Ginsburg-Spanier Theorem to Functions and Mixed Arithmetic
Definable functions in FO(Z,+,≤), FO(R,+,≤) and FO(R,Z,+,≤) are exactly the piecewise-linear or piecewise-simple functions, and mixed sets coincide with semi-polinear sets.
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Computing Thiele Rules on Interval Elections and their Generalizations
Thiele rules are polynomial-time computable on voter interval elections via a standard LP that always has an integral optimum, extending to VCI and LC domains with NP-hardness shown on tree-based generalizations.
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Faster Parameterized Broadcasting
Faster FPT algorithms for Telephone Broadcast achieve 2^{O(vc log vc)}, 2^{O(vi^2 log vi)}, and 2^{O(k log k)} n^{O(1)} time via reduction to b-Matching.
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Optimal Policy Learning under Budget and Coverage Constraints
Optimal policies under budget and coverage constraints admit an affine threshold characterization with O(1) integrality gap in the LP relaxation; two algorithms (GLC and RC) are analyzed with performance guarantees that depend on cost homogeneity and constraint bindingness.