National Repository of Grey Literature 2 records found  Search took 0.01 seconds. 
Two-phase scheduling with unknown speeds
Minařík, Josef ; Sgall, Jiří (advisor) ; Eberle, Franziska (referee)
Speed-robust scheduling is a two-stage scheduling problem with a makespan objective. We are given processing times of n jobs, number of machines m and number of bags b. We have to group the jobs into bags that are to be scheduled on machines of currently unknown speed. The goal is to minimize the worst-case ratio of our makespan and makespan of an adversary who does not have to create bags and assigns jobs directly to machines. So far, the problem has been mostly studied for b = m. We generalize previously known results for infinitesimal jobs (called sand) and prove that the best achievable competitive ratio is mb mb−(m−1)b . We present an algorithm for the case of identical jobs (called bricks) with competitive ratio at most 1.6 in the case b = m, improving the best previously known value of 1.8. We introduce a new category called p-pebbles, those are jobs with processing time at most p times the average load of a machine. Pebbles are half way between sand and the general case (called rocks). We present an algorithm for pebbles that has better robustness factor than the best known algorithm for rocks for small values of p (for p less than 2 − e e−1 in the case b = m). 1
Unfolding some classes of polycubes
Minařík, Josef ; Kynčl, Jan (advisor) ; Tiwary, Hans Raj (referee)
An unfolding of a polyhedron is a cutting along its surface such that the surface remains connected and it can be flattened to the plane without any overlap. An edge- unfolding is a restricted kind of unfolding, we are only allowed to cut along the edges of the faces of the polyhedron. A polycube is a special case of orthogonal polyhedron formed by glueing several unit cubes together face-to-face. In the case of polycubes, the edges of all cubes are available for cuts in edge-unfolding. We focus on one-layer polycubes and present several algorithms to unfold some classes of them. We show that it is possible to edge-unfold any one-layer polycube with cubic holes, thin horizontal holes and separable rectangular holes. The question of edge-unfolding general one-layer polycubes remains open. We also briefly study some classes of multi-layer polycubes. 1

See also: similar author names
2 Minařík, Jakub
3 Minařík, Jan
6 Minařík, Jiří
Interested in being notified about new results for this query?
Subscribe to the RSS feed.