Recognizing unordered depth-first search trees of an undirected graph in parallel

2000 ◽  
Vol 11 (6) ◽  
pp. 559-570 ◽  
Author(s):  
Chen-Hsing Peng ◽  
Biing-Feng Wang ◽  
Jia-Shung Wang
Keyword(s):  
Undirected Graph ◽  
Search Trees ◽  
Depth First Search ◽  
Depth First Search Trees

On the existence of special depth first search trees

1995 ◽  
Vol 19 (4) ◽  
pp. 535-547 ◽  
Author(s):  
Ephraim Korach ◽  
Zvi Ostfeld
Keyword(s):  
Search Trees ◽  
Depth First Search ◽  
Depth First Search Trees

Two Streamlined Depth-First Search Algorithms

1986 ◽  
Vol 9 (1) ◽  
pp. 85-94
Author(s):  
Robert Endre Tarjan
Keyword(s):  
Directed Graph ◽  
Graph Algorithms ◽  
Undirected Graph ◽  
Linear Time ◽  
Search Algorithms ◽  
Depth First Search ◽  
Time Graph

Many linear-time graph algorithms using depth-first search have been invented. We propose simplified versions of two such algorithms, for computing a bipolar orientation or st-numbering of an undirected graph and for finding all feedback vertices of a directed graph.

scholarly journals Space-Efficient Fully Dynamic DFS in Undirected Graphs †

Algorithms ◽  
2019 ◽  
Vol 12 (3) ◽  
pp. 52 ◽  
Author(s):  
Kengo Nakamura ◽  
Kunihiko Sadakane
Keyword(s):  
Undirected Graph ◽  
Undirected Graphs ◽  
Edge Connectivity ◽  
Worst Case ◽  
Depth First Search ◽  
Insertions And Deletions ◽  
Adjacency List ◽  
Graph Traversal ◽  
Dynamic Connectivity ◽  
Traversal Algorithm

Depth-first search (DFS) is a well-known graph traversal algorithm and can be performed in O ( n + m ) time for a graph with n vertices and m edges. We consider the dynamic DFS problem, that is, to maintain a DFS tree of an undirected graph G under the condition that edges and vertices are gradually inserted into or deleted from G. We present an algorithm for this problem, which takes worst-case O ( m n · polylog ( n ) ) time per update and requires only ( 3 m + o ( m ) ) log n bits of space. This algorithm reduces the space usage of dynamic DFS algorithm to only 1.5 times as much space as that of the adjacency list of the graph. We also show applications of our dynamic DFS algorithm to dynamic connectivity, biconnectivity, and 2-edge-connectivity problems under vertex insertions and deletions.

scholarly journals On the star forest polytope for trees and cycles

2019 ◽  
Vol 53 (5) ◽  
pp. 1763-1773
Author(s):  
Meziane Aider ◽  
Lamia Aoudia ◽  
Mourad Baïou ◽  
A. Ridha Mahjoub ◽  
Viet Hung Nguyen
Keyword(s):  
Undirected Graph ◽  
Dominating Set ◽  
Discrete Math ◽  
Complete Characterization ◽  
Facial Structure ◽  
Maximum Weight ◽  
Single Node ◽  
End Node ◽  
Vertex Disjoint

Let G = (V, E) be an undirected graph where the edges in E have non-negative weights. A star in G is either a single node of G or a subgraph of G where all the edges share one common end-node. A star forest is a collection of vertex-disjoint stars in G. The weight of a star forest is the sum of the weights of its edges. This paper deals with the problem of finding a Maximum Weight Spanning Star Forest (MWSFP) in G. This problem is NP-hard but can be solved in polynomial time when G is a cactus [Nguyen, Discrete Math. Algorithms App. 7 (2015) 1550018]. In this paper, we present a polyhedral investigation of the MWSFP. More precisely, we study the facial structure of the star forest polytope, denoted by SFP(G), which is the convex hull of the incidence vectors of the star forests of G. First, we prove several basic properties of SFP(G) and propose an integer programming formulation for MWSFP. Then, we give a class of facet-defining inequalities, called M-tree inequalities, for SFP(G). We show that for the case when G is a tree, the M-tree and the nonnegativity inequalities give a complete characterization of SFP(G). Finally, based on the description of the dominating set polytope on cycles given by Bouchakour et al. [Eur. J. Combin. 29 (2008) 652–661], we give a complete linear description of SFP(G) when G is a cycle.

RCU‐HTM: A generic synchronization technique for highly efficient concurrent search trees

2021 ◽  
Author(s):  
Dimitrios Siakavaras ◽  
Konstantinos Nikas ◽  
Georgios Goumas ◽  
Nectarios Koziris
Keyword(s):  
Search Trees ◽  
Highly Efficient
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