Online Multi-Coloring with Advice

We consider the problem of online graph multi-coloring with advice. Multi-coloring is often used to model frequency allocation in cellular networks. We give several nearly tight upper and lower bounds for the most standard topologies of cellular networks, paths and hexagonal graphs. For the path, negative results trivially carry over to bipartite graphs, and our positive results are also valid for bipartite graphs. The advice given represents information that is likely to be available, studying for instance the data from earlier similar periods of time.Comment: IMADA-preprint-c

Endogenous Market Structures and Strategic Trade Policy

We characterize the optimal export promoting policies for international markets whose structure is endogenous. Contrary to the ambiguous results of strategic trade policy for markets with a fixed number of firms, it is always optimal to subsidize exports as long as entry is endogenous, under both competition in quantities and in prices. With homogenous goods the optimal export subsidy is a fraction 1/€ of the price, where € is the elasticity of demand, the exact opposite of the optimal export tax in the neoclassical trade theory. A similar argument can be applied to show the general optimality of R&D subsidies and of competitive devaluations to promote exports in foreign markets where entry is endogenous.Trade policy, Export Subsidies, Competitive Devaluations, Endogenous Market Structures

Tight bounds on the competitive ratio on accomodating sequences for the seat reservation problem

The unit price seat reservation problem is investigated. The seat reservation problem is the problem of assigning seat numbers on-line to requests for reservations in a train traveling through $k$ stations. We are considering the version where all tickets have the same price and where requests are treated fairly, i.e., a request which can be fulfilled must be granted. For fair deterministic algorithms, we provide an asymptotically matching upper bound to the existing lower bound which states that all fair algorithms for this problem are frac{1{2-competitive on accommodating sequences, when there are at least three seats. Additionally, we give an asymptotic upper bound of frac{7{9 for fair randomized algorithms against oblivious adversaries. We also examine concrete on-line algorithms, First-Fit and Random, for the special case of two seats. Tight analyses of their performance are given