This work charts a nuanced complexity landscape for diameter computation on 2D intersection graphs, delivering new subquadratic algorithms for some object types and diameter values while proving hardness for others under fine-grained assumptions.
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Achieves (2k/3)-approximation for girth in weighted graphs in Õ(m + n^{1+2/k}) time for every k≥2, improving prior partial results, plus new fine-grained lower bounds for unweighted girth approximation.
Credit-based amortized analysis is sound for persistent data structures when credits are stored only on thunks, and Okasaki's debit approach receives a formal operational semantics.
Presents the Cascade Log, a reference-stable tiered append structure using a coalescing interval map for handles, with Θ(A) space, O(log A) point resolution, and sublinear cost on append-dominated histories where A is the fragmentation measure.
citing papers explorer
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Charting the Diameter Computation Landscape on Intersection Graphs in the Plane
This work charts a nuanced complexity landscape for diameter computation on 2D intersection graphs, delivering new subquadratic algorithms for some object types and diameter values while proving hardness for others under fine-grained assumptions.
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Tighter bounds for weighted and unweighted shortest cycle approximation
Achieves (2k/3)-approximation for girth in weighted graphs in Õ(m + n^{1+2/k}) time for every k≥2, improving prior partial results, plus new fine-grained lower bounds for unweighted girth approximation.
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The Cascade Log: Reference-Stable Windowing over Tiered Append Sequences
Presents the Cascade Log, a reference-stable tiered append structure using a coalescing interval map for handles, with Θ(A) space, O(log A) point resolution, and sublinear cost on append-dominated histories where A is the fragmentation measure.