A Rigorous Proof on Circular Wirelength for Hypercubes

نویسندگان

چکیده

We study embeddings of the n-dimensional hypercube into circuit with 2n vertices. prove that circular wirelength attains a minimum by gray coding; was called CT conjecture Chavez and Trapp (Discrete Applied Mathematics, 1998). This problem had claimed to be settled Ching-Jung Guu in her doctoral dissertation “The for hypercubes” (University California, Riverside, 1997). Many argue there are gaps proof. eliminate dissertation.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Exact wirelength of hypercubes on a grid

Grid embeddings are used not only to study the simulation capabilities of a parallel architecture but also to design its VLSI layout. In addition to dilation and congestion, wirelength is an important measure of an embedding. There are very few papers in the literature which provide the exact wirelength of grid embedding. As far as the most versatile architecture hypercube is concerned, only ap...

متن کامل

Embedding hypercubes into cylinders, snakes and caterpillars for minimizing wirelength

We consider the problem of embedding hypercubes into cylinders to minimize the wirelength. Further we show that the edge isoperimetric problem solves the wirelength problem of regular graphs and in particular hypercubes into triangular snakes and caterpillars.

متن کامل

Exact Wirelength of Embedding the Hypercubes into Cycle-of-ladders

Hypercubes are a very popular model for parallel computation because of their regularity and the relatively small number of interprocessor connections. In this paper, we present an algorithm to compute the exact wirelength of embedding the hypercubes into cycle-of-ladders and prove its correctness.

متن کامل

Minimum wirelength of hypercubes into n-dimensional grid networks

In the paper [Exact wirelength of hypercube on a grid, Discrete Applied Mathematics, 157 (2009), no. 7, 1486 1495], the minimum wirelength of an -dimensional hypercube into a 2b2c £ 2d2e grid has been obtained. In this paper, we obtain the same when the 2b2c £ 2d2e rectangular grid is replaced by a generalized grid of size 21 £ 22 £ ¢ ¢ ¢ £ 2 where 1 + 2 + +  = , 1 · 2 · ¢ ¢...

متن کامل

Circular wirelength of Generalized Petersen Graphs

In this paper we formulate the Vertex Congestion Lemma leading to a new technique in computing the exact wirelength of an embedding. We compute the circular wirelength of generalized Petersen graphs by partitioning the vertices as well as the edges of cycles. Further we obtain the linear wirelength of circular ladders. Our algorithms produce optimal values in linear time.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Acta Mathematica Scientia

سال: 2023

ISSN: ['1572-9087', '0252-9602']

DOI: https://doi.org/10.1007/s10473-023-0223-3