5 papers
Towards Learning-Guided Discovery of Extremal Geometric Constructions: A PatternBoost Study
Deepak Ajwani, Paula Carroll, Rishikesh Gajjala +5
Extremal constructions play a central role in the design and analysis of algorithms. Integrality-gap instances expose the limitations of relaxations, while hard configurations reve…
Random Garbage Separates XOR from Forward-Only Queries
Khaled Elbassioni, Rishikesh Gajjala, Saurabh Ray
We give exponential quantum query separations between the standard XOR interface and two forward-only interfaces that supply neither an adjoint nor an inverse oracle. Let $X=\F_2^n…
Tight Approximation Thresholds for Geometric Stabbing
Khaled Elbassioni, Rishikesh Gajjala, Saurabh Ray
We study geometric covering problems: stabbing axis-parallel squares and cubes by coordinate hyperplanes, stabbing horizontal segments by horizontal and vertical lines, and transve…
Counterexamples to Wegner's Conjecture for Rectangles
Deepak Ajwani, Rishikesh Gajjala, Rajiv Raman +1
Wegner conjectured in 1965 that every finite family of axis-parallel rectangles satisfies , where is the minimum num…
Learning to Prune Instances of Steiner Tree Problem in Graphs
Jiwei Zhang, Deepak Ajwani
We consider the Steiner tree problem on graphs where we are given a set of nodes and the goal is to find a tree sub-graph of minimum weight that contains all nodes in the given set…