VPG and EPG bend-numbers of Halin graphs
Maximum Independent Set on B_1 B 1 -VPG Graphs
The NP-completeness of the decision version restricted to unit length equilateral B1-VPG graphs is established and the approximation algorithms presented are shown to have an approximation guarantee of Ologd.
Geometric Dominating Set and Set Cover via Local Search
This paper proves that the popular local search algorithm leads to an $(1+\varepsilon)$ approximation when objects are homothetic set of convex objects in n time, significantly improving the best known approximation guarantees.
Approximation schemes for bounded distance problems on fractionally treewidth-fragile graphs
This work gives polynomial-time approximation schemes for monotone maximization problems expressible in terms of distances and efficiently solvable in graphs of bounded treewidth and provides quasipolynomial-time approximate schemes for these problems in all classes with sublinear separators.
Circular Separation Dimension of a Subclass of Planar Graphs
- Arpitha P. Bharathi, Minati De, Abhiruk Lahiri
- MathematicsDiscret. Math. Theor. Comput. Sci.
- 30 December 2016
It is shown that if $G$ is $2$-outerplanar then $\pi^\circ(G) = 2$ and it is proved that if £G is a series-parallel graph then $G \leq 2$, which means that every pair of non-adjacent edges is separated in at least one of the circular orderings.
On Comparable Box Dimension
Two boxes in R are comparable if one of them is a subset of a translation of the other one. The comparable box dimension of a graph G is the minimum integer d such that G can be represented as a…
Hardness and approximation for L-EPG and B1-EPG graphs
On Chromatic Number of (n, m)-graphs
On approximating MIS over B1-VPG graphs
Reconfiguring Shortest Paths in Graphs
- Kshitij Gajjar, A. Jha, Manish Kumar, Abhiruk Lahiri
- Computer Science, MathematicsAAAI
- 14 December 2021
It is shown that (a) is intractable, even for relaxed variants of the problem, and generalise the problem to when at most k contiguous vertices on a shortest path can be changed at a time.