scholarly journals I/O efficient algorithms for the minimum cut problem on unweighted undirected graphs

2015 ◽  
Vol 575 ◽  
pp. 33-41 ◽  
Author(s):  
Alka Bhushan ◽  
G. Sajith
Keyword(s):  
Efficient Algorithms ◽  
Minimum Cut ◽  
Undirected Graphs ◽  
Minimum Cut Problem

scholarly journals A Linear Time Algorithm for a Variant of the MAX CUT Problem in Series Parallel Graphs

2017 ◽  
Vol 2017 ◽  
pp. 1-4 ◽  
Author(s):  
Brahim Chaourar
Keyword(s):  
Linear Time ◽  
Maximum Flow ◽  
Time Algorithm ◽  
Minimum Cut ◽  
Linear Time Algorithm ◽  
Induced Subgraphs ◽  
Positive Weight ◽  
Max Cut Problem ◽  
In Series ◽  
Minimum Cut Problem

Given a graph G=V,E, a connected sides cut U,V\U or δU is the set of edges of E linking all vertices of U to all vertices of V\U such that the induced subgraphs GU and GV\U are connected. Given a positive weight function w defined on E, the maximum connected sides cut problem (MAX CS CUT) is to find a connected sides cut Ω such that wΩ is maximum. MAX CS CUT is NP-hard. In this paper, we give a linear time algorithm to solve MAX CS CUT for series parallel graphs. We deduce a linear time algorithm for the minimum cut problem in the same class of graphs without computing the maximum flow.

A fast algorithm for the generalized parametric minimum cut problem and applications

Algorithmica ◽  
1992 ◽  
Vol 7 (1-6) ◽  
pp. 499-519 ◽  
Author(s):  
Dan Gusfield ◽  
Charles Martel
Keyword(s):  
Fast Algorithm ◽  
Minimum Cut ◽  
Minimum Cut Problem

Max Horn SAT and the minimum cut problem in directed hypergraphs

1998 ◽  
Vol 80 (2) ◽  
pp. 213-237 ◽  
Author(s):  
G. Gallo ◽  
C. Gentile ◽  
D. Pretolani ◽  
G. Rago
Keyword(s):  
Minimum Cut ◽  
Directed Hypergraphs ◽  
Minimum Cut Problem

MOD-2 INDEPENDENCE AND DOMINATION IN GRAPHS

2000 ◽  
Vol 11 (03) ◽  
pp. 355-363 ◽  
Author(s):  
MAGNÚS M. HALLDÓRSSON ◽  
JAN KRATOCHVÍL ◽  
JAN ARNE TELLE
Keyword(s):  
Efficient Algorithms ◽  
Existence Problem ◽  
Combinatorial Interpretation ◽  
Undirected Graphs ◽  
Gauss Elimination ◽  
Np Complete ◽  
Domination In Graphs

We develop an O(n3) algorithm for deciding if an n-vertex digraph has a subset of vertices with the property that each vertex of the graph has an even number of arcs into the subset. This algorithm allows us to give a combinatorial interpretation of Gauss-Jordan and Gauss elimination on square boolean matrices. In addition to solving this independence-mod-2 (even) set existence problem we also give efficient algorithms for related domination-mod-2 (odd) set existence problems on digraphs. However, for each of the four combinations of these two properties we show that even though the existence problem on digraphs is tractable, the problems of deciding the existence of a set of size exactly k, larger than k, or smaller than k, are all NP-complete for undirected graphs.

scholarly journals Network flow optimization for restoration of images

2002 ◽  
Vol 2 (4) ◽  
pp. 199-218 ◽  
Author(s):  
Boris A. Zalesky
Keyword(s):  
Ising Model ◽  
Network Flow ◽  
Minimum Cut ◽  
Optimization Approach ◽  
Gray Scale ◽  
Flow Optimization ◽  
Binary Images ◽  
Statistical Background ◽  
Network Flow Optimization ◽  
Minimum Cut Problem

The network flow optimization approach is offered for restoration of gray-scale and color images corrupted by noise. The Ising models are used as a statistical background of the proposed method. We present the new multiresolution network flow minimum cut algorithm, which is especially efficient in identification of the maximum a posteriori (MAP) estimates of corrupted images. The algorithm is able to compute the MAP estimates of large-size images and can be used in a concurrent mode. We also consider the problem of integer minimization of two functions,U1(x)=λ∑i|yi−xi|+∑i,j  βi,j|xi−xj|andU2(x)=∑i λi (yi−xi)2+∑i,j  βi,j (xi−xj)2, with parametersλ,λi,βi,j>0and vectorsx=(x1,…,xn),y=(y1,…,yn)∈{0,…,L−1}n. Those functions constitute the energy ones for the Ising model of color and gray-scale images. In the caseL=2, they coincide, determining the energy function of the Ising model of binary images, and their minimization becomes equivalent to the network flow minimum cut problem. The efficient integer minimization ofU1(x),U2(x)by the network flow algorithms is described.

scholarly journals Assembly Synthesis With Subassembly Partitioning for Optimal In-Process Dimensional Adjustability

2003 ◽  
Author(s):  
Byungwoo Lee ◽  
Kazuhiro Saitou
Keyword(s):  
Early Stage ◽  
Minimum Cut ◽  
Weighted Graphs ◽  
Systematic Method ◽  
Critical Dimensions ◽  
Structural Assembly ◽  
Optimization Routine ◽  
Complex Structural ◽  
Minimum Cut Problem

Achieving the dimensional integrity for a complex structural assembly is a demanding task due to the manufacturing variations of parts and the tolerance relationship between them. While assigning tight tolerances to all parts would solve the problem, an economical solution is taking advantage of small motions that joints allow, such that critical dimensions are adjusted during assembly processes. This paper presents a systematic method that decomposes product geometry at an early stage of design, selects joint types, and generates subassembly partitioning to achieve the adjustment of the critical dimensions during assembly processes. A genetic algorithm (GA) generates candidate assemblies based on a joint library specific for an application domain. Each candidate assembly is evaluated by an internal optimization routine that computes the subassembly partitioning for optimal in-process adjustability, by solving an equivalent minimum cut problem on weighted graphs. A case study on a 3D automotive space frame with the accompanying joint library is presented.

Sign in / Sign up

Export Citation Format

Share Document