arXiv subjects

Igor Malinović

Publications and source records attributed to Igor Malinović.

2 recordsLinked to original sources

arXiv2018

On bounded pitch inequalities for the min-knapsack polytope

In the min-knapsack problem one aims at choosing a set of objects with minimum total cost and total profit above a given threshold. In this paper, we study a class of valid inequalities for min-knapsack known as bounded pitch inequalities, which generalize the well-known unweighted cover inequalities. While separating over pitch-1 inequalities is NP-hard, we show that approximate separation over the set of pitch-1 and pitch-2 inequalities can be done in polynomial time. We also investigate integrality gaps of linear relaxations for min-knapsack when these inequalities are added. Among other results, we show that, for any fixed $t$, the $t$-th CG closure of the natural linear relaxation has the unbounded integrality gap.

cs.DS↗

arXiv2015

Clustered planarity testing revisited

The Hanani--Tutte theorem is a classical result proved for the first time in the 1930s that characterizes planar graphs as graphs that admit a drawing in the plane in which every pair of edges not sharing a vertex cross an even number of times. We generalize this result to clustered graphs with two disjoint clusters, and show that a straightforward extension to flat clustered graphs with three or more disjoint clusters is not possible. For general clustered graphs we show a variant of the Hanani--Tutte theorem in the case when each cluster induces a connected subgraph. Di Battista and Frati proved that clustered planarity of embedded clustered graphs whose every face is incident with at most five vertices can be tested in polynomial time. We give a new and short proof of this result, using the matroid intersection algorithm.

cs.CG↗