Improved and Generalized Algorithms for Burning a Planar Point Set

Given a set P of points in $$\mathbb {R}^2$$ , point burning process is discrete time to burn all the where fires must be initiated at P. Specifically, starts with single burnt from P, and each subsequent step, burns that are within one unit distance currently points, as well other unburnt (if exists). The number smallest steps required If we allow fire anywhere then called an process. One can think problem finding minimum integer r such covered disks radii $$0,1,2,\ldots r$$ . A provides simple model for distributing commodities locations by sending daily bulk shipment distribution center, i.e., place initiate fire. corresponds days reach locations. In this paper show both problems admit PTAS dimension. We two dimensions, $$(1.96+\varepsilon )$$ $$(1.92+\varepsilon approximable, respectively, every $$\varepsilon >0$$ which improves previously known $$(2+\varepsilon approximation these problems. generalize results allowing have different spreading rates, prove even if sources given input, sequence itself NP-hard. Finally, obtain 2-approximation maximum steps.