Efficient, incremental coverage of space with a continuous curve

Efficient, incremental coverage of space with a continuous curve

This paper is concerned with algorithmic techniques for the incremental generation of continuous curves that can efficiently cover an abstract surface. We introduce the notion of low-discrepancy curves as an extension of the notion of low-discrepancy sequences—such that sufficiently smooth curves with low-discrepancy properties can be defined and generated. We then devise a procedure for liftin...

Solving Continuous POMDPs: Value Iteration with Incremental Learning of an Efficient Space Representation

Discrete POMDPs of medium complexity can be approximately solved in reasonable time. However, most applications have a continuous and thus uncountably infinite state space. We propose the novel concept of learning a discrete representation of the continuous state space to solve the integrals in continuous POMDPs efficiently and generalize sparse calculations over the continuous space. The repre...

Efficient Coverage Directed State Space Search

Efficient elliptic curve cryptosystems

Elliptic curve cryptosystems (ECC) are new generations of public key cryptosystems that have a smaller key size for the same level of security. The exponentiation on elliptic curve is the most important operation in ECC, so when the ECC is put into practice, the major problem is how to enhance the speed of the exponentiation. It is thus of great interest to develop algorithms for exponentiation...

Onion Curve: A Space Filling Curve with Near-Optimal Clustering

Space filling curves (SFCs) are widely used in the design of indexes for spatial and temporal data. Clustering is a key metric for an SFC, that measures how well the curve preserves locality in moving from higher dimensions to a single dimension. We present the onion curve, an SFC whose clustering performance is provably close to optimal for cube and nearcube shaped query sets, irrespective of ...