the first provable approximation guarantees for efficient algorithms. Using an analysis framework based on submodular functions, we show that a natural greedy strategy obtains a solution that is provably within 63 % of optimal for several classes of models; our framework suggests a general approach

that respect the metric of the (possibly weighted) graph. Given a graph G we map its vertices to a normed space in an attempt to (i) Keep down the dimension of the host space and (ii) Guarantee a small distortion, i.e., make sure that distances between vertices in G closely match the dis-tances between

We motivate and develop a natural bicriteria measure for assessing the quality of a clustering which avoids the drawbacks of existing measures. A simple recursive heuristic is shown to have poly-logarithmic worst-case guarantees under the new measure. The main result of the paper is the analysis

for a given upper bound on the error. Under the assumption that finding optimal bucket boundaries is computationally inefficient, previous research has focused on heuristics with no provable bounds on the quality of the solutions. In this paper, we present algorithms for computing optimal bucket

The field programmable gate-array (FPGA) has become an important technology in VLSI ASIC designs. In the past a few years, a number of heuristic algorithms have been proposed for technology mapping in lookup-table (LUT) based FPGA designs, but none of them guarantees optimal solutions for general

. The first method, which is guaranteed to be optimal, reduces running time by structuring the search space so that a modified depth-first search usually avoids even considering allocations that contain conflicting bids. Caching and pruning are also used to speed searching. Our second method is a heuristic

coloring and minimum dominating set. We also present an on-line coloring heuristic which achieves a competitive ratio of 6 for unit disk graphs. Our heuristics do not need a geometric representation of unit disk graphs. Geometric representations are used only in establishing the performance guarantees

We present a new heuristic point-to-point shortest path algorithm based on contraction hierarchies (CH). Given an ε ≥ 0, we can prove that the length of the path computed by our algorithm is at most (1 + ε) times the length of the optimal (shortest) path. Exact CH is based on node contraction

be fully guaranteed a priori. Therefore, the number of nodes that must be deployed in order to completely cover the whole monitored area is often higher than if a deterministic procedure were used. In networks with stochastically placed nodes, activating only the necessary number of sensor nodes at any

Daniel Berend* Steven S. Skiena t 1