We give the first polynomial-time approximation scheme (PTAS) for the Steiner forest problem on planar graphs and, more generally, on graphs of bounded genus. As a first step, w...
This paper focuses on the assignment of discrete points among K robots and determining the order in which the points should be processed by the robots, in the presence of geometric...
Nilanjan Chakraborty, Srinivas Akella, John T. Wen
Soss proved that it is NP-hard to find the maximum flat span of a fixed-angle polygonal chain: the largest distance achievable between the endpoints in a planar embedding. These f...
We consider the problem of finding a balanced ordering of the vertices of a graph. More precisely, we want to minimise the sum, taken over all vertices v, of the difference betwe...
We give a surprisingly short proof that in any planar arrangement of Ò curves where each pair intersects at most a fixed number (×) of times, the -level has subquadratic (Ç´...