25,215 research outputs found
Lower Bounds for On-line Interval Coloring with Vector and Cardinality Constraints
We propose two strategies for Presenter in the on-line interval graph
coloring games. Specifically, we consider a setting in which each interval is
associated with a -dimensional vector of weights and the coloring needs to
satisfy the -dimensional bandwidth constraint, and the -cardinality
constraint. Such a variant was first introduced by Epstein and Levy and it is a
natural model for resource-aware task scheduling with different shared
resources where at most tasks can be scheduled simultaneously on a single
machine.
The first strategy forces any on-line interval coloring algorithm to use at
least different colors on an -colorable set of intervals. The second strategy forces any
on-line interval coloring algorithm to use at least
different colors on an
-colorable set of unit intervals
Subelliptic SpinC Dirac Operators, IV Proof of the Relative Index Conjecture
We prove the relative index conjecture, which in turn implies that the set of
embeddable deformations of a strictly pseudoconvex CR-structure on a compact
3-manifold is closed in the C\infty-topology.Comment: 5 page
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