Fei-Huang Chang

Wide-sense nonblocking for symmetric or asymmetric 3-stage Clos networks under various routing strategies

Benes established the notion of wide-sense nonblocking by constructing an example on the symmetric 3-stage Clos network under packing which requires less hardware compared to strict nonblocking. This has remained the only example of a wide-sense non-blocking 3-stage Clos network which is not strictly nonblocking. In this paper, we study packing as well as several other routing strategies which have been studied in the literature and proved that no other example exists for the symmetric 3-stage Clos network. We then extend the study to asymmetric 3-stage Clos network for the first time. In particular, we extend Benes example to asymmetric 3-stage Clos network and show that these are the only two possible examples for the strategies under study.

The identification of positive clones in a general inhibitor model

In using pooling designs to identify clones containing a specific subsequence called positive clones, sometimes there exist nonpositive clones which can cancel the effect of positive clones. Various models have been studied which differ in the power of cancellation. Although the various models pose interesting mathematical problems, and ingenious constructions of pooling designs have been proposed, in practice we rarely are sure about the true model and thus about which pooling design to use. In this paper we give a pooling design which fits all inhibitor models, and does not use more tests than in the more specific models. In particular, we obtain a 1-round pooling design for the k-inhibitor model for which only sequential designs are currently known.

All-to-all broadcast problem of some classes of graphs under the half duplex all-port model

Abstract All-to-all communication occurs in many important applications in parallel processing. In this paper, we study the all-to-all broadcast number (the shortest time needed to complete the all-to-all broadcast) of graphs under the assumption that: each vertex can use all of its links at the same time, and each communication link is half duplex and can carry only one message at a unit of time. We give upper and lower bounds for the all-to-all broadcast number of graphs and give formulas for the all-to-all broadcast number of trees, complete bipartite graphs and double loop networks under this model.

Wide-sense nonblocking for multi-log d N networks under various routing strategies

Chang et al. showed that the number of middle switches required for WSNB under strategies: save the unused, packing, minimum index, cyclic dynamic, and cyclic static, for the 3-stage Clos network C(n, m, r) with r ≥ 3 is the same as required for SNB. In this paper, we prove the same conclusion for the multi-logd N network. We also extend our results, except for the minimum index strategy, to a general class of networks including the 3-stage Clos network and the multi-logd N network as special cases.

Pooling designs for clone library screening in the inhibitor complex model

In this paper we introduce inhibitors into the complex model and we give a lower bound and an upper bound of tests in a nonadaptive pooling design for some inhibitor complex model. We propose a very efficient pooling design for the general inhibitor complex model and extend it to the error-tolerant case.

All-to-all broadcast problems on Cartesian product graphs

All-to-all communication occurs in many important applications in parallel processing. In this paper, we study the all-to-all broadcast number (the shortest time needed to complete the all-to-all broadcast) of Cartesian product of graphs under the assumption that: each vertex can use all of its links at the same time, and each communication link is half duplex and can carry only one message at a unit of time. We give upper and lower bounds for the all-to-all broadcast number of Cartesian product of graphs and give formulas for the all-to-all broadcast numbers of some classes of graphs, such as the Cartesian product of two cycles, the Cartesian product of a cycle with a complete graph of odd order, the Cartesian product of two complete graphs of odd order, and the hypercube Q 2 n under this model.

L ( 2 , 1 ) -labelings of subdivisions of graphs

Given a graph G and a function h from E ( G ) to N , the h -subdivision of G , denoted by G ( h ) , is the graph obtained from G by replacing each edge u v in G with a path P : u x u v 1 x u v 2 ? x u v n - 1 v , where n = h ( u v ) . When h ( e ) = c is a constant for all e ? E ( G ) , we use G ( c ) to replace G ( h ) . Given a graph G , an L ( 2 , 1 ) -labeling of G is a function f from the vertex set V ( G ) to the set of all nonnegative integers such that | f ( x ) - f ( y ) | ? 2 if d G ( x , y ) = 1 , and | f ( x ) - f ( y ) | ? 1 if d G ( x , y ) = 2 . A k - L ( 2 , 1 ) -labeling is an L ( 2 , 1 ) -labeling such that no label is greater than k . The L ( 2 , 1 ) -labeling number of G , denoted by λ ( G ) , is the smallest number k such that G has a k - L ( 2 , 1 ) -labeling. We study the L ( 2 , 1 ) -labeling numbers of subdivisions of graphs in this paper. We prove that λ ( G ( 3 ) ) = Δ ( G ) + 1 for any graph G with Δ ( G ) ? 4 , and show that λ ( G ( h ) ) = Δ ( G ) + 1 if Δ ( G ) ? 5 and h is a function from E ( G ) to N so that h ( e ) ? 3 for all e ? E ( G ) , or if Δ ( G ) ? 4 and h is a function from E ( G ) to N so that h ( e ) ? 4 for all e ? E ( G ) .

Supermodularity in Mean-Partition Problems*

Supermodularity of the λ function which defines a permutation polytope has proved to be crucial for the polytope to have some nice fundamental properties. Supermodularity has been established for the λ function for the sum-partition problem under various models. On the other hand, supermodularity has not been established for the mean-partition problem even for the most basic labeled single-shape model. In this paper, we fill this gap and also settle for all other models except one. We further extend our results to other types of supermodularity.

Families of Subsets Without a Given Poset in Double Chains and Boolean Lattices

Given a finite poset P, the intensively studied quantity La(n, P) denotes the largest size of a family of subsets of [n] not containing P as a weak subposet. Burcsi and Nagy (J. Graph Theory Appl. 1, 40–49 2013) proposed a double-chain method to get an upper bound La(n,P)≤12(|P|+h−2)n⌊n/2⌋

Multigroup Testing for Items With Real-Valued Status Under Standard Arithmetic

{\mathrm La}(n,P)\le \frac {1}{2}(|P|+h-2)\left (\begin {array}{c}n \\ \lfloor {n/2}\rfloor \end {array}\right )