Efficient algorithms for combinatorial problems on graphs with bounded decomposability — A survey

1985 ◽  
Vol 25 (1) ◽  
pp. 1-23 ◽  
Author(s):  
Stefan Arnborg
Keyword(s):  
Efficient Algorithms ◽  
Combinatorial Problems

scholarly journals Algorithms for Weighted Independent Transversals and Strong Colouring

2022 ◽  
Vol 18 (1) ◽  
pp. 1-16
Author(s):  
Alessandra Graf ◽  
David G. Harris ◽  
Penny Haxell
Keyword(s):  
Existence Theorems ◽  
Sufficient Conditions ◽  
Randomized Algorithm ◽  
Independent Set ◽  
Deterministic Algorithm ◽  
Efficient Algorithms ◽  
Combinatorial Problems ◽  
Vertex Partition ◽  
Partition Class ◽  
Strong Chromatic Number

An independent transversal (IT) in a graph with a given vertex partition is an independent set consisting of one vertex in each partition class. Several sufficient conditions are known for the existence of an IT in a given graph and vertex partition, which have been used over the years to solve many combinatorial problems. Some of these IT existence theorems have algorithmic proofs, but there remains a gap between the best existential bounds and the bounds obtainable by efficient algorithms. Recently, Graf and Haxell (2018) described a new (deterministic) algorithm that asymptotically closes this gap, but there are limitations on its applicability. In this article, we develop a randomized algorithm that is much more widely applicable, and demonstrate its use by giving efficient algorithms for two problems concerning the strong chromatic number of graphs.

scholarly journals Getting new algorithmic results by extending distance-hereditary graphs via split composition

2021 ◽  
Vol 7 ◽  
pp. e627
Author(s):  
Serafino Cicerone ◽  
Gabriele Di Stefano
Keyword(s):  
Chromatic Number ◽  
Domination Number ◽  
Graph Isomorphism ◽  
Clique Number ◽  
Efficient Algorithms ◽  
Combinatorial Problems ◽  
Stability Number ◽  
New Class ◽  
Graph Classes ◽  
Graph Class

In this paper, we consider the graph class denoted as Gen(∗;P3,C3,C5). It contains all graphs that can be generated by the split composition operation using path P3, cycle C3, and any cycle C5 as components. This graph class extends the well-known class of distance-hereditary graphs, which corresponds, according to the adopted generative notation, to Gen(∗;P3,C3). We also use the concept of stretch number for providing a relationship between Gen(∗;P3,C3) and the hierarchy formed by the graph classes DH(k), with k ≥1, where DH(1) also coincides with the class of distance-hereditary graphs. For the addressed graph class, we prove there exist efficient algorithms for several basic combinatorial problems, like recognition, stretch number, stability number, clique number, domination number, chromatic number, and graph isomorphism. We also prove that graphs in the new class have bounded clique-width.

Tidal Flow: A Fast and Teachable Maximum Flow Algorithm

2018 ◽  
Vol 12 ◽  
pp. 25-41
Author(s):  
Matthew C. FONTAINE
Keyword(s):  
Computer Science ◽  
Tidal Flow ◽  
Maximum Flow ◽  
Efficient Algorithms ◽  
Science Students ◽  
Flow Algorithm ◽  
Maximum Flows

Among the most interesting problems in competitive programming involve maximum flows. However, efficient algorithms for solving these problems are often difficult for students to understand at an intuitive level. One reason for this difficulty may be a lack of suitable metaphors relating these algorithms to concepts that the students already understand. This paper introduces a novel maximum flow algorithm, Tidal Flow, that is designed to be intuitive to undergraduate andpre-university computer science students.

Energy-Efficient Algorithms for Distributed File System HDFS

2014 ◽  
Vol 36 (5) ◽  
pp. 1047-1064 ◽  
Author(s):  
Bin LIAO ◽  
Jiong YU ◽  
Tao ZHANG ◽  
Xing-Yao YANG
Keyword(s):  
Energy Efficient ◽  
File System ◽  
Efficient Algorithms ◽  
Distributed File System

Network Energy Consumption Models and Energy Efficient Algorithms

2012 ◽  
Vol 35 (3) ◽  
pp. 603-615 ◽  
Author(s):  
Fa ZHANG ◽  
Antonio Fernandez Anta ◽  
Lin WANG ◽  
Chen-Ying HOU ◽  
Zhi-Yong LIU
Keyword(s):  
Energy Consumption ◽  
Energy Efficient ◽  
Efficient Algorithms
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