Succinct navigational oracles for families of intersection graphs on a circle

Succinct Coverage Oracles

In this paper, we identify a fundamental algorithmic problem that we term succinct dynamic covering (SDC), arising in many modern-day web applications, including ad-serving and online recommendation systems in eBay and Netflix. Roughly speaking, SDC applies two restrictions to the well-studied Max-Coverage problem [9]: Given an integer k, X = {1, 2, . . . , n} and I = {S1, . . . , Sm}, Si ⊆ X ,...

On cycles in intersection graphs of rings

‎Let $R$ be a commutative ring with non-zero identity. ‎We describe all $C_3$‎- ‎and $C_4$-free intersection graph of non-trivial ideals of $R$ as well as $C_n$-free intersection graph when $R$ is a reduced ring. ‎Also, ‎we shall describe all complete, ‎regular and $n$-claw-free intersection graphs. ‎Finally, ‎we shall prove that almost all Artin rings $R$ have Hamiltonian intersection graphs. ...

The Speeds of Families of Intersection Graphs

A fundamental question of graph theory lies in counting the number of graphs which satisfy certain properties. In particular, the structure of intersection graphs of planar curves is unknown, and Schaefer, Sedgwick, and Štefankovič have shown that recognizing such graphs is NP-complete. As such, the number of intersection graphs of planar curves poses an interesting problem. Pach and Tóth have ...

A Note on Succinct Representations of Graphs

Intersection Graphs for Families of Balls in Rn

1. INTRODUCTION If F is a finite family of sets, then the intersection graph r(F) is the graph with vertex-set F and edges the unordered pairs C, D of distinct elements of F such that C n D # 0. It is easy to see [6, p. 19] that every graph G is isomorphic to some intersection graph T(F). Some interesting classes of graphs have arisen by letting F range over families of balls in some metric spa...