We investigate the problem of simultaneously dominating all spanning trees a given graph. prove that on 2-connected graphs, subset vertices dominates graph if and only it is vertex cover. Using this fact we present an exact algorithm finds simultaneous set minimum size using oracle for finding The can be implemented to run in polynomial time several classes, such as bipartite or chordal graphs....

A collection of races in a single election can be audited as a group by auditing a random sample of batches of ballots and combining observed discrepancies in the races represented in those batches in a particular way: the maximum across-race relative overstatement of pairwise margins (MARROP). A risk-limiting audit for the entire collection of races can be built on this ballot-based auditing u...

In the integrated vehicle and crew scheduling problem (VCSP) one has to simultaneously assign vehicles to timetabled trips and drivers to vehicles. In this paper two integer linear programming formulations are used to describe the integrated problem. On both formulations the multi-depot vehicle scheduling problem is modeled as a multicommodity flow problem while the crew scheduling problem is m...