Tighter approximation bounds for LPT scheduling in two special cases

Tighter Bounds for Graph Steiner Tree Approximation

The classical Steiner tree problem in weighted graphs seeks a minimum weight connected subgraph containing a given subset of the vertices (terminals). We present a new polynomialtime heuristic that achieves a best-known approximation ratio of 1 + ln 3 2 ≈ 1.55 for general graphs, and best-known approximation ratios of ≈ 1.28 for quasi-bipartite graphs (i.e., where no two non-terminals are adjac...

Tighter Lower Bounds for Scheduling Problems in High-level Synthesis

This paper presents new results on lower bounds for the scheduling problem in high-level synthesis. While several techniques exist for lower bound estimation, comparisons among the techniques have been experimental with few guarantees on the quality of the bounds. In this paper, we present new bounds and a theoretical comparison of these with existing bounds. For the resource-constrained schedu...

List Scheduling and LPT

Tighter Bounds for Facility Games

In facility games, public facilities are placed based on the reported locations of the agents. The cost of an agent is measured by the distance from its location to the nearest facility. In this paper, we consider the one dimensional facility games where all locations for agents and the facilities are on the real line. We study the approximation ratio of social welfare for strategy-proof mechan...

Tighter Bounds for Structured Estimation

Large-margin structured estimation methods work by minimizing a convex upper bound of loss functions. While they allow for efficient optimization algorithms, these convex formulations are not tight and sacrifice the ability to accurately model the true loss. We present tighter non-convex bounds based on generalizing the notion of a ramp loss from binary classification to structured estimation. ...