Ordered Binary Decision Diagrams (OBDDs for short) are popular dynamic data structures for Boolean functions. In some modern applications, we have to handle such huge graphs that the usual explicit representations by adjacency lists or adjacency matrices are infeasible. To deal with such huge graphs, OBDD-based graph representations and algorithms have been investigated. Although the size of OB...

An intriguing theme in graph theory is that of the intersection graph of a family of subsets of a set: the vertices of the graph are represented by the subsets of the family and adjacency is defined by a non-empty intersection of the corresponding subsets. Prime examples are interval graphs and chordal graphs. An interval graph is the intersection graph of a family of closed intervals on the re...

In this paper we consider the problem of privately computing the intersection of sets (setintersection), as well as several variations on this problem: cardinality set-intersection, threshold set-intersection, and over-threshold set-intersection. Cardinality set-intersection is the problem of determining the size of the intersection set, without revealing the actual threshold set. In threshold ...

In this paper we describe an algorithm for producing infinitely many examples of set-theoretic complete intersection monomial curves in P n+1 , starting with a single set-theoretic complete intersection monomial curve in P n. Moreover we investigate the numerical criteria to decide when these monomial curves can or cannot be obtained via semigroup gluing.

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...

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...

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...