We consider the Hypergraph Multiway Partition problem (Hyper-MP). The input consists of an edge-weighted hypergraph G = (V, E) and k vertices s1, . . . , sk called terminals. A multiway partition of the hypergraph is a partition (or labeling) of the vertices of G into k sets A1, . . . , Ak such that si ∈ Ai for each i ∈ [k]. The cost of a multiway partition (A1, . . . , Ak) is ∑k i=1 w(δ(Ai)), ...

Congestion minimization is a well-known routing problem for which there is an O(logn/ log logn)approximation via randomized rounding [17]. Srinivasan [18] formally introduced the low-congestion multi-path routing problem as a generalization of the (single-path) congestion minimization problem. The goal is to route multiple disjoint paths for each pair, for the sake of fault tolerance. Srinivasa...

Multilayer soft lithography (MSL) provides a convenient and low-cost method for fabricating poly(dimethyl siloxane) (PDMS) microfluidic devices with on-chip valves for automated and precise control of fluid flow. MSL casting molds for flow channels typically incorporate small patches of rounded positive photoresist at valve locations to achieve the rounded cross-sectional profile required for t...

Rounding a real-valued matrix to an integer one such that the rounding errors in all rows and columns are less than one is a classical problem. It has been applied to hypergraph coloring, in scheduling and in statistics. Here, it often is also desirable to round each entry randomly such that the probability of rounding it up equals its fractional part. This is known as unbiased rounding in stat...

This dissertation studies the market microstructure of over-the-counter markets. All three chapters are based on the municipal (tax-exempt) bond market. However, the implications on price formation, price discovery and dealer’s market power can be generalized into the other OTC markets such as corporate bond and derivatives markets as well. In the first chapter “Price Clustering and Dealer’s Ma...

This paper investigates the localization within the Xenopus egg of the factors responsible for the periodic activities such as the cyclic rounding-up and flattening, related to the cleavage cycle. Denuded eggs were bisected along the boundary line between the animal and the vegetal hemispheres immediately after being rotated through 90 degrees off the vertical axis (Early Bisection). The result...