On VLSI layouts of the star graph and related networks
نویسندگان
چکیده
We prove that the minimal VLSI layout of the arrangement graph A(n; k) occupies (n!=(n ? k ? 1)!) 2 area. As a special case we obtain an optimal layout for the star graph S n with the area (n!) 2 : This answers an open problem posed by Ak-ers, Harel and Krishnamurthy 1]. The method is also applied to the pancake graph. The results provide optimal upper and lower bounds for crossing numbers of the above graphs.
منابع مشابه
The Recursive Grid Layout Scheme for VLSI Layout of Hierarchical Networks
We propose the recursive grid layout scheme for deriving efficient layouts of a variety of hierarchical networks and computing upper bounds on the VLSI area of general hierarchical networks. In particular, we construct optimal VLSI layouts for butterfly networks, generalized hypercubes, and star graphs that have areas within a factor of 1+ o(1) from their lower bounds. We also derive efficient ...
متن کاملVLSI Layouts of Complete Graphs and Star Graphs
In this paper, we present efficient layouts for complete graphs and star graphs. We show that an N-node complete graph can be optimally laid out using LN2/4] tracks for a colinear layout, and can be laid out in N4/16 + o(N4) area for a 2D layout. We also show that an N-node star graph can be laid out in N2/16 + o(N2) area, which is smaller than any possible layout of a similar-size hypercube. T...
متن کاملBisection widths of transposition graphs and their applications
We prove lower and upper bounds on bisection widths of the transposition graphs. This class of graphs contains several frequently studied interconnection networks including star graphs and hypercubes. In particular, we prove that the bisection width of the complete transposition graph is of order (n:n!) which solves the open problem (R) 3.356 of the Leighton's book 11] and determine nearly exac...
متن کاملBisection widths of transposition graphs
We prove lower and upper bounds on bisection widths of the transposition graphs. This class of graphs contains several frequently studied intercon-nection networks including star graphs and hypercubes. In particular, we prove that the bisection width of the complete transposition graph is of order (n:n!) which solves the open problem (R) 3.356 of the Leighton's book 10] and determine nearly exa...
متن کاملEfficient VLSI Layouts of Hypercubic Networks
In this paper, we present efficient VLSI layouts of several hypercubic networks. We show that an N-node hypercube and an N-node cube-connected cycles (CCC) graph can be laid out in 4N2=9 + o(N2) and 4N2=(9log22 N) + o(N2= log2 N) areas, respectively, both of which are optimal within a factor of 1:7̄+ o(1). We introduce the multilayer grid model, and present efficient layouts of hypercubes that u...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Integration
دوره 17 شماره
صفحات -
تاریخ انتشار 1994