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You would say that algorithm A is better than algorithm B if it has a smaller ratio.However there are situations where two algorithms have the same ratio, still in practice one is better than the other.For each customer, there is a critical time within which a service must be repeated.Given the travelling time between the customers, the set of customers is partitioned so that each subset is served by one agent in a cyclic manner without violating any individual critical time requirement. As an example, we consider a problem, in which a fleet of unmanned aerial vehicles is used for area patrolling.In this presentation, we discuss various connections between unions and intersections of maximum (critical) independent sets of graphs, which lead to deeper understanding of crown structures, in general, and König-Egerváry graphs, in particular.Abstract: The relocation problem is formulated from a municipal redevelopment project in east Boston.So people came up with a different technique to compare online algorithms directly with each other, rather than through the optimal offline solution. I would do a survey on this technique, and talk about a related personal work: Best-of-two-worlds analysis of online search, with Spyros Angelopoulos and Shendan Jin.
Abstract: While the problem of scheduling unit-time jobs with release dates and deadlines on parallel machines is polynomially solvable via a reduction to the assignment problem, the no-idle requirement destroys this reduction and makes the problem challenging.Crowns are also accepted as important tools for fixed parameter tractable problems.For instance, the size of the vertex cover can be substantially reduced by deleting both the vertices of a crown and its neighborhood.Actually, every critical independent set is contained in a maximum independent set, while a maximum critical independent set can be found in polynomial time.If S is an independent set such that there is a matching from its neighborhood into S, then it is a crown.