5 papers
On Linear-Size Guillotine-Separable Subsets of Fat Convex Objects, Disks, and Squares
Mark de Berg, Debajyoti Kar, Arindam Khan +1
Let be a family of pairwise disjoint objects in the plane. We say that a subset is \emph{separable} if it admits a sequence of gu…
Approximation Schemes and Structural Barriers for the Two-Dimensional Knapsack Problem with Rotations
Debajyoti Kar, Arindam Khan, Andreas Wiese
We study the two-dimensional (geometric) knapsack problem with rotations (2DKR), in which we are given a square knapsack and a set of rectangles with associated profits. The object…
Improved Approximation Algorithms for Three-Dimensional Knapsack
Klaus Jansen, Debajyoti Kar, Arindam Khan +2
We study the three-dimensional Knapsack (3DK) problem, in which we are given a set of axis-aligned cuboids with associated profits and an axis-aligned cube knapsack. The objective…
Improved Approximation Algorithms for Three-Dimensional Bin Packing
Debajyoti Kar, Arindam Khan, Malin Rau
We study two fundamental three-dimensional (3D) geometric packing problems: 3D (Geometric) Bin Packing (3D-BP), and 3D Minimum Volume Bounding Box (3D-MVBB), where given a set of 3…
Random-Order Online Independent Set of Intervals and Hyperrectangles
Mohit Garg, Debajyoti Kar, Arindam Khan
In the Maximum Independent Set of Hyperrectangles problem, we are given a set of (possibly overlapping) -dimensional axis-aligned hyperrectangles, and the goal is to find a…