In contrast with the scalar-weighted networks, where bipartite consensus can be achieved if and only underlying signed network is structurally balanced, structural balance property no longer a graph-theoretic equivalence to in case of matrix-weighted networks. To re-establish relationship between structure solution, non-trivial balancing set introduced which edges whose sign negation transform ...

Privacy-preserving techniques for processing sets of information have attracted the research community’s attention in recent years due to society’s increasing dependency on availability data at any time. One fundamental problems set operations is known as Private Set Intersection (PSI). The pro...

Secure Multi-party Computation (SMPC) is a family of protocols which allow some parties to compute function on their private inputs, obtaining the output at end and nothing more. In this work, we focus particular SMPC problem named Private Set Intersection (PSI). The challenge in PSI how two or more can intersection input sets, while elements that are not remain private. This has attracted atte...

The objective of this section is to introduce notation and theoretical tools regarding structural models and bipartite graphs that will be used in proofs of results in coming section. The structural representation of a set of equations M with unknown variables X is a bipartite graph with variables and equations as node sets. There is an edge in the graph between a node representing an equation ...

Orthogonal ray graphs are the intersection graphs of horizontal and vertical rays (i.e. half-lines) in the plane. If the rays can have any possible orientation (left/right/up/down) then the graph is a 4-directional orthogonal ray graph (4-DORG). Otherwise, if all rays are only pointing into the positive x and y directions, the intersection graph is a 2-DORG. Similarly, for 3-DORGs, the horizont...

In this paper, we present an O(r n) algorithm for the linear matroid parity problem. Our solution technique is to introduce a modest generalization, the non-simple parity problem, and identify an important subclass of non-simple parity problems called 'easy' parity problems which can be solved as matroid intersection problems. We then show how to solve any linear matroid parity problem parametr...

The constantly increasing dependence on anytime-anywhere availability of data and the commensurately increasing fear of losing privacy motivate the need for privacy-preserving techniques. One interesting and common problem occurs when two parties need to privately compute an intersection of their respective sets of data. In doing so, one or both parties must obtain the intersection (if one exis...