We consider the practical problem of constructing binary space partitions (BSPs) for a set S of n orthogonal, nonintersecting, two-dimensional rectangles in IR3 such that the aspect ratio of each rectangle in S is at most , for some constant 1. We present an n2O(plogn )-time algorithm to build a binary space partition of size n2O(plogn ) for S. We also show that if m of the n rectangles in S ha...

A special case of an elegant result due to Anderson proves that the number of (s, s + 1)-core partitions is finite and is given by the Catalan number Cs. Amdeberhan recently conjectured that the number of (s, s + 1)-core partitions into distinct parts equals the Fibonacci number Fs+1. We prove this conjecture by enumerating, more generally, (s, ds− 1)-core partitions into distinct parts. We do ...

We study basis partitions, introduced by Hansraj Gupta in 1978. For this family of partitions, we give a recurrence, a generating function, identities relating basis partitions to more familiar families of partitions, and a new characterization of basis partitions.

In this paper, we develop a simple technique for constructing a Binary Space Partition (BSP) for a set of orthogonal rectangles in R 3. Our algorithm has the novel feature that it tunes its performance to the geometric properties of the rectangles, e.g., their aspect ratios. We have implemented our algorithm and tested its performance on real data sets. We have also systematically compared the ...

In this paper, we give combinatorial proofs and new generalizations of q-series identities of Dilcher and Uchimura related to divisor function. Some interesting combinatorial results related to partition and arm length are also presented.

We present a general method for evaluating and visualizing evolutionary dynamics of self-replicators using a graph-based representation for genealogy. Through a transformation from the space of species and mutations to the space of nodes and links, evolutionary dynamics are understood as a flow in graph space. Mapping functions are introduced to translate graph nodes to points in an n-dimension...

 Mobile sensor networks rely heavily on inter-sensor connectivity for collection of data. Nodes in these networks monitor different regions of an area of interest and collectively present a global overview of some monitored activities or phenomena. A failure of a sensor leads to loss of connectivity and may cause partitioning of the network into disjoint segments. A number of approaches have be...

Cost partitioning is a general and principled approach for constructing additive admissible heuristics for state-space search. Cost partitioning approaches for optimal classical planning include optimal cost partitioning, uniform cost partitioning, zero-one cost partitioning, saturated cost partitioning, post-hoc optimization and the canonical heuristic for pattern databases. We compare these a...

In domains such as robotic rescue, robots must plan paths through environments that are complex and dynamic, and in which robots have only incomplete knowledge. This will normally require both diversions from planned paths as well as significant re-planning as events in the domain unfold and new information is acquired. In terms of a representation for path planning, these requirements place si...

In this paper we present statistical timing driven hMetisbased partitioning. We approach timing driven partitioning from a different perspective: we use the statistical timing criticality concept to change the partitioning process itself. We exploit the hyperedge coarsening scheme of the hMetis partitioner for our timing minimization purpose. This allows us to perform partitioning such that the...