Computing Set Intersection privately and efficiently between two mutually mistrusting parties is an important basic procedure in the area of private data mining. Assuring robustness, namely, coping with potentially arbitrarily misbehaving (i.e., malicious) parties, while retaining protocol efficiency (rather than employing costly generic techniques) is an open problem. In this work the first so...

Let two linear matroids have the same rank in matroid intersection. A maximum linear matroid intersection (maximum linear matroid parity set) is called a basic matroid intersection (basic matroid parity set), if its size is the rank of the matroid. We present that enumerating all basic matroid intersections (basic matroid parity sets) is in NC, provided that there are polynomial bounded basic m...

Let H,K be subgroups of G. We investigate the intersection properties of left and right cosets of these subgroups. If H and K are subgroups of G, then G can be partitioned as the disjoint union of all left cosets of H, as well as the disjoint union of all right cosets of K. But how do these two partitions of G intersect each other? Definition 1. Let G be a group, and H a subgroup of G. A left t...

As with many min-max characterizations, proving one of the inequalities is straightforward. For any U ⊆ S and I ∈ I1 ∩ I2, we have |I| = |I ∩ U |+ |I ∩ (S \ U)| ≤ r1(U) + r2(S \ U), since I ∩ U is an independent set in I1 and I ∩ (S \ U) is an independent set in I2. Therefore, maxI∈I1∩I2 |I| ≤ minU∈S (r1(U) + r2(S \ U)). The following important examples illustrate some of the applications of th...

A representation scheme for general polyhedra in arbitrary dimensions is presented. Each polyhedron is represented as a convex chain, i.e. an algebraic sum of convex polyhedra (cells). Each cell in turn is represented as the intersection of halfspaces and encoded in a vector. The notion of vertices is abandoned completely. It is shown how this approach allows the decomposition of set operations...

A natural way to deal with multiple, partially conflicting objectives is turning all the objectives but one into budget constraints. Some classical polynomial-time optimization problems, such as spanning tree and forest, shortest path, (perfect) matching, independent set (basis) in a matroid or in the intersection of two matroids, become NP-hard even with one budget constraint. Still, for most ...

Boxicity of a graph G(V, E) is the minimum integer k such that G can be represented as the intersection graph of axis parallel boxes in Rk. Cubicity is a variant of boxicity, where the axis parallel boxes in the intersection representation are restricted to be of unit length sides. Deciding whether boxicity (resp. cubicity) of a graph is at most k is NP-hard, even for k = 2 or 3. Computing thes...

In this paper we initialize the study of independent domination in directed graphs. We show that an independent dominating set of an orientation of a graph is also an independent dominating set of the underlying graph, but that the converse is not true in general. We then prove existence and uniqueness theorems for several classes of digraphs including orientations of complete graphs, paths, tr...

In CAD/CAM modeling, objects are represented using the Boundary Representation (ANSI Brep) model. Detection of possible intersection between objects can be based on the objects’ boundaries (i.e., triangulated surfaces), and computed using triangle-triangle intersection. Usually only a cross intersection algorithm is needed; however, it is beneficial to have a single robust and fast intersection...

This research examined how environmental attributes near intersections influence the perceived crash risk among school-aged children, which provides information on the potential risks of pedestrian crashes that can guide the development of proactive countermeasures. In a sample of 799 children aged 10-12 years old in Korea, the environmental attributes of intersections perceived as having a hig...