An O ( n ^ 4 ) time algorithm to compute the bisection width of solid grid graphs
نویسندگان
چکیده
The bisection problem asks for a partition of the n vertices of a graph into two sets of size at most dn/2e, so that the number of edges connecting the two sets is minimised. A grid graph is a finite connected subgraph of the infinite two-dimensional grid. It is called solid if it has no holes. Papadimitriou and Sideri [7] gave an O(n) time algorithm to solve the bisection problem on solid grid graphs. We propose a novel approach that exploits structural properties of optimal cuts within a dynamic program. We show that our new technique leads to an O(n)
منابع مشابه
An O(n) Time Algorithm to Compute the Bisection Width of Solid Grid Graphs
The bisection problem asks for a partition of the n vertices of a graph into two sets of size at most dn/2e, so that the number of edges connecting the two sets is minimised. A grid graph is a finite connected subgraph of the infinite two-dimensional grid. It is called solid if it has no holes. Papadimitriou and Sideri [7] gave an O(n) time algorithm to solve the bisection problem on solid grid...
متن کاملOn the VLSI Area and Bisection Width of Star Graphs and Hierarchical Cubic Networks
We solve an open question posed by Akers and Krishnamurthy in 1986 [1, 3] concerning VLSI layout of star graphs. We show that the area of the optimal layout of an N-node star graph, hierarchical cubic network (HCN), or hierarchical folded-hypercube network (HFN) is N2=16 o(N2) under the Thompson model, or under the extended grid model where a node occupies a rectangle of sides that may range fr...
متن کاملGraph Bisection AlgoriLhrns With Good A-veragc Case Behavior
In the paper, we describe a polynomial time algorithm that, for every input graph, either outputs the minimum bisection of the graph or halts without output. More importantly, we show that the algorithm chooses the former course with high probability for many natural classes of graphs. In particular, for every fixed d 2 3, all suffciently large n and all b = o(nl l / lT j ) , the algorithm find...
متن کاملBounds on the max and min bisection of random cubic and random 4-regular graphs
In this paper, we present a randomized algorithm to compute the bisection width of cubic and 4-regular graphs. The analysis of the proposed algorithms on random graphs provides asymptotic upper bounds for the bisection width of random cubic and random 4-regular graphs with n vertices, giving upper bounds of 0:174039n for random cubic, and of 0:333333n for random 4-regular. We also obtain asympt...
متن کاملGraph bisection algorithms
In this thesis, we describe a polynomial time algorithm that, for every input graph, either outputs the minimum bisection of the graph or halts without output. More importantly, we show that the algorithm chooses the former course with high probability for many natural classes of graphs. In particular, for every fixed d > 3, all sufficiently large n and all b = o(ni-1/d2lJ), the algorithm finds...
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:
دوره شماره
صفحات -
تاریخ انتشار 2011