Abs-t-We study the problem of running full binary tree based algorithms on a hypercube with faulty nodes. The key to this problem is to devise a method for embedding a full binary tree into the faulty hypercube. Based on a novel embedding strategy, we present two results for embedding an (n-1)-tree (a full binary tree with 2"-l-1 nodes) into an n-cube (a hypercube with 2" nodes) with unit dilat...

Given a family of feasible subsets of a ground set, the packing problem is to find a largest subfamily of pairwise disjoint family members. Non-approximability renders heuristics attractive viable options, while efficient methods with worst-case guarantee are a key concern in computational complexity. This work proposes a novel near-Boolean optimization method relying on a polynomial multilinea...

Given a list of d-dimensional cuboid items with associated profits, the orthogonal knapsack problem asks for a packing of a selection with maximal profit into the unit cube. We restrict the items to hypercube shapes and derive a ( 5 4 + )-approximation for the twodimensional case. In a second step we generalize our result to a ( 2 +1 2d + )approximation for d-dimensional packing.

SSOR preconditioning of fermion matrix inversions which is parallelized using a locally-lexicographic lattice sub-division has been shown to be very efficient for standard Wilson fermions. We demonstrate here the power of this method for the Sheikholeslami-Wohlert improved fermion action and for a renormalization group improved action incorporating couplings of the lattice fermion fields up to ...

The double-rooted complete binary tree is a complete binary tree where the path (of length ) between the children of the root is replaced by a path of length . It is folklore that the double-rooted complete binary tree is a spanning tree of the hypercube of the same size. Unfortunately, the usual construction of an embedding of a double-rooted complete binary tree into the hypercube does not pr...

We consider operators acting on convex subsets of the unit hypercube. These operators are used in constructing convex relaxations of combinatorial optimization problems presented as a 0,1 integer programming problem or a 0,1 polynomial optimization problem. Our focus is mostly on operators that, when expressed as a lift-and-project operator, involve the use of semidefiniteness constraints in th...

The RACE-Hypercube Processor is a highly parallel signal processor with fourteen degrees of freedom in selecting parallel operations. The fourteen degrees of freedom include the ability to select the 1) number of very long instruction word (VLIW) slots, 2) number and type of application specific instructions, 3) number and type of application specific processing element (PE) hardware assists, 4...

BACKGROUND It has been shown that the clinical state of one patient can be represented by known measured variables of interest, each of which then form the element of a fuzzy set as point in the unit hypercube. We hypothesized that precise comparison of a single patient with the average patient of a large double blind controlled randomized study is possible using fuzzy theory. METHODS/PRINCIP...

This paper introduces a new interconnection network topology called Balanced Varietal Hypercube (BVH), suitable for massively parallel systems. The proposed topology being a hybrid structure retains almost all the attractive properties of Balanced Hypercube and Varietal Hypercube. The topology, various parameters, routing and broadcasting of Balanced Varietal Hypercube are presented. The perfor...