Almost Linear Time Algorithms for Minsum k-Sink Problems on Dynamic Flow Path Networks

AbstractMotivated by evacuation planning, several problems regarding dynamic flow networks have been studied in recent years. A dynamic flow network consists of an undirected graph with positive edge lengths, positive edge capacities, and positive vertex weights. The road network in an area can be treated as a graph where the edge lengths are the distances along the roads and the vertex weights are the number of people at each site. An edge capacity limits the number of people that can enter the edge per unit time. In a dynamic flow network, when particular points on edges or vertices called sinks are given, all of the people are required to evacuate from the vertices to the sinks as quickly as possible. This chapter gives an overview of two of our recent results on the problem of locating multiple sinks in a dynamic flow path network such that the max/sum of evacuation times for all the people to sinks is minimized, and we focus on techniques that enable the problems to be solved in almost linear time.

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Linear time algorithms for linear programming

Computers & Mathematics with Applications ◽

10.1016/s0898-1221(99)00069-3 ◽

1999 ◽

Vol 37 (4-5) ◽

pp. 199-208

Author(s):

E.A. Galperin

Keyword(s):

Linear Programming ◽

Linear Time ◽

Linear Time Algorithms

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Almost-linear-time algorithms for Markov chains and new spectral primitives for directed graphs

Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing - STOC 2017 ◽

10.1145/3055399.3055463 ◽

2017 ◽

Cited By ~ 14

Author(s):

Michael B. Cohen ◽

Jonathan Kelner ◽

John Peebles ◽

Richard Peng ◽

Anup B. Rao ◽

...

Keyword(s):

Markov Chains ◽

Linear Time ◽

Directed Graphs ◽

Linear Time Algorithms

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Linear-Time Algorithms for Tree Root Problems

Algorithmica ◽

10.1007/s00453-013-9815-y ◽

2013 ◽

Vol 71 (2) ◽

pp. 471-495 ◽

Cited By ~ 1

Author(s):

Maw-Shang Chang ◽

Ming-Tat Ko ◽

Hsueh-I Lu

Keyword(s):

Linear Time ◽

Linear Time Algorithms

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FAULT TOLERANT ROUTING IN HYPERCUBES AND STAR GRAPHS

Parallel Processing Letters ◽

10.1142/s0129626496000133 ◽

1996 ◽

Vol 06 (01) ◽

pp. 127-136 ◽

Cited By ~ 5

Author(s):

QIAN-PING GU ◽

SHIETUNG PENG

Keyword(s):

Free Path ◽

Fault Tolerant ◽

Linear Time ◽

Time Efficiency ◽

Routing Problem ◽

Star Graphs ◽

Linear Time Algorithms ◽

Better Than

In this paper, we give two linear time algorithms for node-to-node fault tolerant routing problem in n-dimensional hypercubes Hn and star graphs Gn. The first algorithm, given at most n−1 arbitrary fault nodes and two non-fault nodes s and t in Hn, finds a fault-free path s→t of length at most [Formula: see text] in O(n) time, where d(s, t) is the distance between s and t. Our second algorithm, given at most n−2 fault nodes and two non-fault nodes s and t in Gn, finds a fault-free path s→t of length at most d(Gn)+3 in O(n) time, where [Formula: see text] is the diameter of Gn. When the time efficiency of finding the routing path is more important than the length of the path, the algorithms in this paper are better than the previous ones.

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Fun with Sub-linear Time Algorithms

Lecture Notes in Computer Science - Fun with Algorithms ◽

10.1007/978-3-540-72914-3_3 ◽

2007 ◽

pp. 15-15

Author(s):

Luca Trevisan

Keyword(s):

Linear Time ◽

Linear Time Algorithms

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Linear-time algorithms for programming cellular permutation arrays

Proceedings of the 1986 ACM fourteenth annual conference on Computer science - CSC '86 ◽

10.1145/324634.325222 ◽

1986 ◽

Cited By ~ 1

Author(s):

A. Yavuz Oruc ◽

M. Yaman Oruc

Keyword(s):

Linear Time ◽

Permutation Arrays ◽

Linear Time Algorithms

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In-Place Linear-Time Algorithms for Euclidean Distance Transform

Transactions on Computational Science VIII - Lecture Notes in Computer Science ◽

10.1007/978-3-642-16236-7_7 ◽

2010 ◽

pp. 103-113 ◽

Cited By ~ 1

Author(s):

Tetsuo Asano ◽

Hiroshi Tanaka

Keyword(s):

Euclidean Distance ◽

Linear Time ◽

Distance Transform ◽

Euclidean Distance Transform ◽

Linear Time Algorithms

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Efficient Web Mining for Traversal Path Patterns

Web Mining ◽

10.4018/978-1-59140-414-9.ch015 ◽

2011 ◽

pp. 322-338 ◽

Cited By ~ 1

Author(s):

Zhixiang Chen ◽

Richard H. Fowler ◽

Ada Wai-Chee Fu ◽

Chunyue Wang

Keyword(s):

Web Mining ◽

Linear Time ◽

Fundamental Problem ◽

A Priori ◽

Web Pages ◽

Suffix Trees ◽

Web Logs ◽

Large Alphabet ◽

Optimal Linear ◽

Linear Time Algorithms

A maximal forward reference of a Web user is a longest consecutive sequence of Web pages visited by the user in a session without revisiting some previously visited page in the sequence. Efficient mining of frequent traversal path patterns, that is, large reference sequences of maximal forward references, from very large Web logs is a fundamental problem in Web mining. This chapter aims at designing algorithms for this problem with the best possible efficiency. First, two optimal linear time algorithms are designed for finding maximal forward references from Web logs. Second, two algorithms for mining frequent traversal path patterns are devised with the help of a fast construction of shallow generalized suffix trees over a very large alphabet. These two algorithms have respectively provable linear and sublinear time complexity, and their performances are analyzed in comparison with the a priori-like algorithms and the Ukkonen algorithm. It is shown that these two new algorithms are substantially more efficient than the a priori-like algorithms and the Ukkonen algorithm.

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