Lower bounds for searching robots, some faulty

Lower Bounds for Searching Robots, some Faulty

Suppose we are sending out k robots from 0 to search the real line at constant speed (with turns) to find a target at an unknown location; f of the robots are faulty, meaning that they fail to report the target although visiting its location (called crash type). The goal is to find the target in time at most λ|d|, if the target is located at d, |d| ≥ 1, for λ as small as possible. We show that ...

Some Lower Bounds for Estrada Index

Some lower bounds for the $L$-intersection number of graphs

‎For a set of non-negative integers~$L$‎, ‎the $L$-intersection number of a graph is the smallest number~$l$ for which there is an assignment of subsets $A_v subseteq {1,dots‎, ‎l}$ to vertices $v$‎, ‎such that every two vertices $u,v$ are adjacent if and only if $|A_u cap A_v|in L$‎. ‎The bipartite $L$-intersection number is defined similarly when the conditions are considered only for the ver...

some lower bounds for estrada index

Lower Bounds on Fast Searching

Given a graph, suppose that intruders hide on vertices or along edges of the graph. The fast searching problem is to find the minimum number of searchers required to capture all intruders satisfying the constraint that every edge is traversed exactly once and searchers are not allowed to jump. In this paper, we prove lower bounds on the fast search number. We present a linear time algorithm to ...