Field-Programmable Gate Arrays (FPGAs) are flexible and reusable circuits that can be easily reconfigured by the designer. One of the steps involved in the logic design with FPGA circuits is placement. In this step, the logic functions are assigned to specific cells of the circuit. In this paper we present a placement algorithm for FPGA circuits. In traditional min-cut based placement algorithm...

The well-known Max Cut problem asks for the largest bipartite subgraph of a graph G. This problem has been the subject of extensive research, both from the algorithmic perspective in computer science and the extremal perspective in combinatorics. Let n be the number of vertices and e be the number edges of G and let b(G) denote the size of the largest bipartite subgraph of G. The extremal part ...

We analyze the addition of a simple local improvement step to various known ran-domized approximation algorithms. Let ' 0:87856 denote the best approximation ratio currently known for the Max Cut problem on general graphs GW95]. We consider a semideenite relaxation of the Max Cut problem, round it using the random hyperplane rounding technique of ((GW95]), and then add a local improvement step....

This paper studies the existence of eecient (small size) ampliiers for proving explicit inaproximability results for bounded degree and bounded occurrence combinatorial optimization problems, and gives an explicit construction for such ampliiers. We use this construction to improve the currently best known approximation lower bounds for bounded occurrence instances of linear equations mod 2, an...

Metric MAX-CUT is the problem of dividing a set of points in metric space into two parts so as to maximize the sum of the distances between points belonging to distinct parts. We show that metric MAX-CUT has a polynomial time randomized approximation scheme.

Performance of cooperative diversity schemes at Low Signal to Noise Ratios (LSNR) was recently studied by Avestimehr et. al. [1] who emphasized the importance of diversity gain over multiplexing gain at low SNRs. It has also been pointed out that continuous energy transfer to the channel is necessary for achieving the max-flow min-cut bound at LSNR. Motivated by this we propose the use of Selec...

Improved inaproximability results are given, including the best up to date explicit approximation thresholds for bounded occurence sat-issability problems, like MAX-2SAT and E2-LIN-2, and problems in bounded degree graphs, like MIS, Node Cover and MAX CUT. We prove also for the rst time inapproximability of the problem of Sorting by Reversals and display an explicit approximation threshold for ...

We prove that the max-cut and max-bisection problems are NP-hard on unit disk graphs. We also show that λ-precision graphs are planar for λ > 1/ √ 2 and give a dichotomy theorem for max-cut computational complexity on λ-precision unit disk graphs.

We give a simple proof for the sample complexity bound O (1/ε4) of absolute approximation of MAX-CUT. The proof depends on a new analysis method for linear programs (LPs) underlying MAX-CUT which could be also of independent interest.

We show that the following two problems are polynomiaUy equivalent: 1) Given a (weighted) graph G, and a cut C of G, decide whether C is maximal or not . 2) Given a (weighted) graph G, and a cut C of G, decide whether C is maximal or not , and in case it is not , find a better solution C'. As a consequence, an optimali ty testing oracle may be used to design a polynomial t ime algori thm for ap...