For given a pair of nodes in a graph, the minimum non-separating path problem looks for a minimum weight path between the two nodes such that the remaining graph after removing the path is still connected. The balanced connected bipartition (BCP2) problem looks for a way to bipartition a graph into two connected subgraphs with their weights as equal as possible. In this paper we present an O(N ...

Given a large edge-weighted network G with k vertices designated as terminals, we wish to compress it and store, using little memory, the value of the minimum cut (or equivalently, maximum flow) between every bipartition of terminals. One appealing methodology to implement a compression of G is to construct a mimicking network : a small network G′ with the same k terminals, in which the minimum...

We consider the problem of bipartitioning a circuit into two balanced components that minimizes the number of crossing nets. Previously, the Kernighan and Lin type (K&L) heuristics, the simulated annealing approach, and the spectral method were given to solve the problem. However, network ow techniques were overlooked as a viable approach to min-cut balanced bipartition due to its high complexi...

Given a large edge-weighted network G with k terminal vertices, we wish to compress it and store, using little memory, the value of the minimum cut (or equivalently, maximum flow) between every bipartition of terminals. One appealing methodology to implement a compression of G is to construct a mimicking network : a small network G′ with the same k terminals, in which the minimum cut value betw...

In this paper we investigate the bipartite analogue of strong Erdos-Hajnal property. We prove that for every forest $H$ and $\tau>0$ there exists $\epsilon>0$, such if $G$ has a bipartition $(A,B)$ does not contain as an induced subgraph, at most $(1-\tau)|A|\cdot|B|$ edges, then is stable set in contains least $\epsilon|V_i|$ vertices $V_i$, $i=1,2$. No graphs except forests have

We analyze fermions after an interaction quantum quench in one spatial dimension and study the growth of steady state entanglement entropy density under either a mode or particle bipartition. For integrable lattice models we find excellent agreement between increase entropy, for chaotic examination two further neighbor strengths suggests similar correspondence. This result highlights applicabil...

Given a tree T on n vertices and a set P of n points in the plane in general position, it is known that T can be straight line embedded in P without crossings. The problem becomes more diicult if T is rooted and we want to root it at any particular point of P. The problem in this form was posed by Perles and partially solved by Pach and Torosick 5]. A complete solution was found by Ikebe et al....