An induced packing of odd cycles in a graph is a packing such that there is no edge in the graph between any two odd cycles in the packing. We prove that the problem is solvable in time O(n ) when the input graph is planar. We also show that deciding if a graph has an induced packing of two odd cycles is NP-complete.

One of the main issues in addressing three-dimensional packing problems is finding an efficient and accurate definition of the points where to place the items inside the bins. The performance of exact and heuristic methods is actually strongly influenced by the choice of a placement rule. We introduce the Extreme Point concept and present a new Extreme Point-based rule for packing items inside ...

In the present research, the aqueous suspensions of nano-sized YSZ particles were prepared using a common and available dispersant (Dolapix CE64) at different pH values and their stability were evaluated through the sedimentation height, viscosity measurement, and microstructural observation. Different amounts of dispersant were tested and the optimum percentage was examined by measuring the vi...

Bin packing is a well studied problem which has many applications. In this paper we design a robust APTAS for the problem. The robust APTAS receives a single input item to be added to the packing at each step. It maintains an approximate solution throughout this process, by slightly adjusting the solution for each new item. At each step, the total size of items which may migrate between bins mu...

A new short proof is given for Brandt and Harrington's theorem about conformal uniformizations of planar nitely connected domains as domains with boundary components of speciied shapes. This method of proof generalizes to periodic domains. Letting the uniformized domains degenerate in a controlled manner, we deduce the existence of packings of speciied shapes and with speciied combinatorics. Th...

A first-order expansion of the R-vector space structure on R does not define every compact subset of every Rn if and only if topological and Hausdorff dimension coincide on all closed definable sets. Equivalently, if A ⊆ Rk is closed and the Hausdorff dimension of A exceeds the topological dimension of A, then every compact subset of every Rn can be constructed from A using finitely many boolea...