Set It and Forget It: Approximating the Set Once Strip Cover Problem

Approximating Min - sum Set Cover 1 Uriel

The Pipelined Set Cover Problem

A classical problem in query optimization is to find the optimal ordering of a set of possibly correlated selections. We provide an abstraction of this problem as a generalization of set cover called pipelined set cover, where the sets are applied sequentially to the elements to be covered and the elements covered at each stage are discarded. We show that several natural heuristics for this NP-...

Identifying Codes and the Set Cover Problem

We consider the problem of finding a minimum identifying code in a graph, i.e., a designated set of vertices whose neighborhoods uniquely overlap at any vertex on the graph. This identifying code problem was initially introduced in 1998 and has been since fundamentally connected to a wide range of applications, including fault diagnosis, location detection, environmental monitoring, and connect...

Forget It!

We encountered the need for a theory of forgetting in our work on Cognitive Robotics. 1 In our effort to control an autonomous robot, we imagine the robot has a knowledge base representing the initial world state. As the robot performs actions, she needs to bring the knowledge base up to date. To do so, she needs to forget about all the facts that are no longer true, and in such a way that this...

Algorithms for connected set cover problem and fault-tolerant connected set cover problem

Given a set V of elements, S a family of subsets of V , and G a connected graph on vertex set S,a connected set cover (CSC) is a subfamily R of S such that every element in V is covered by at least one set of R, and the subgraph G[R] of G induced by R is connected. If furthermore G[R] is k-connected and every element in V is covered by at least m sets inR, thenR is a (k,m)-CSC. In this paper, w...