Fast edge searching and fast searching on graphs

Fast-Mixed Searching on Graphs

We introduce the fast-mixed search model, which is a combination of the fast search model and the mixed search model. We establish relations between the fast-mixed search problem and other graph search problems. We also establish relations between the fast-mixed search problem and the inducedpath cover problem. We present linear-time algorithms for computing the fast-mixed search number and opt...

Fast-mixed searching and related problems on graphs

Edge searching weighted graphs

In traditional edge searching one tries to clean all of the edges in a graph employing the least number of searchers. It is assumed that each edge of the graph initially has a weight equal to one. In this paper we modify the problem and introduce the Weighted Edge Searching Problem by considering graphswith arbitrary positive integerweights assigned to its edges. We give bounds on the weighted ...

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 ...

Fast String Searching

Since the Boyer-Moore algorithm was described in 1977, it has been the standard benchmark for the practical string search literature. Yet this yardstick compares badly with current practice. We describe two algorithms that perform 47% fewer comparisons and are about 4.5 times faster across a wide range of architectures and compilers. These new variants are members of a family of algorithms base...