Colored Packets with Deadlines and Metric Space Transition Cost

We consider scheduling of colored packets with transition costs which form a general metric space. We design 1 − O (√ MST (G) L ) competitive algorithm. Our main result is an hardness result of 1 − Ω (√ MST (G) L ) which matches the competitive ratio of the algorithm for each metric space separately. In particular we improve the hardness result of Azar at el. for uniform metric space. We also extend our result for a weighted directed graph with triangular inequality and show 1 − O (√ TSP (G) L ) competitive algorithm and nearly matching hardness result. In proving our hardness results we use some interesting non-standard embedding.