Olive oil mill wastewater (OMW), known in Lebanon as Zibar, is one of the two by-products obtained during olive oil extraction. OMW represents a serious environmental pollution problem especially for underground and surface ...

We study a pair of N P-hard problems aimed at finding small sets of faces in planar graphs. In the disk dimension problem, we are given a planar graph G, and seek the least number k for which G embeds in the plane minus k ...

With respect to a given plane graph, G, a face cover is defined as a set of faces whose boundaries collectively contain every vertex in G. It is known that, when k is fixed, finding a cover of size k (if indeed any exist) ...

A variety of efficient kernelization strategies for the classic vertex cover problem are developed, implemented and compared experimentally. A new technique, termed crown reduction, is introduced and analyzed. Applications ...

Graph-theoretical approaches to biological network analysis have proven to be effective for small networks but are computationally infeasible for comprehensive genome-scale systems-level elucidation of these networks. The ...

The notion of a “problem kernel” plays a central role in the design of fixed-parameter algorithms. The FPT literature is rich in kernelization algorithms that exhibit fundamentally different approaches. We highlight ...

We present a reduction procedure that takes an arbitrary instance of the 3-Set Packing problem and produces an equivalent instance whose number of elements is bounded by a quadratic function of the input parameter. Such ...

Many exact algorithms for NPNP -hard graph problems adopt the old Davis-Putman branch-and-reduce paradigm. The performance of these algorithms often suffers from the increasing number of graph modifications, such as ...

Current generation supercomputers have over one million cores awaiting highly demanding computations and applications. An area that could largely benefit from such processing capabilities is naturally that of exact algorithms ...