scholarly journals The Inverse 1-Median Problem on Tree Networks with Variable Real Edge Lengths

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Longshu Wu ◽  
Joonwhoan Lee ◽  
Jianhua Zhang ◽  
Qin Wang
Keyword(s):  
Location Problem ◽  
Hamming Distance ◽  
Linear Time ◽  
Shopping Centers ◽  
Median Problem ◽  
Tree Networks ◽  
Total Cost ◽  
Negative Edge ◽  
Polynomial Time Algorithms ◽  
Np Hardness

Location problems exist in the real world and they mainly deal with finding optimal locations for facilities in a network, such as net servers, hospitals, and shopping centers. The inverse location problem is also often met in practice and has been intensively investigated in the literature. As a typical inverse location problem, the inverse 1-median problem on tree networks with variable real edge lengths is discussed in this paper, which is to modify the edge lengths at minimum total cost such that a given vertex becomes a 1-median of the tree network with respect to the new edge lengths. First, this problem is shown to be solvable in linear time with variable nonnegative edge lengths. For the case when negative edge lengths are allowable, the NP-hardness is proved under Hamming distance, and strongly polynomial time algorithms are presented underl1andl∞norms, respectively.

scholarly journals k-Approximate Quasiperiodicity Under Hamming and Edit Distance

Algorithmica ◽  
2021 ◽  
Author(s):  
Aleksander Kędzierski ◽  
Jakub Radoszewski
Keyword(s):  
Lower Bounds ◽  
Polynomial Time ◽  
Edit Distance ◽  
Hamming Distance ◽  
Efficient Algorithms ◽  
Np Hard ◽  
Total Cost ◽  
Polynomial Time Algorithms ◽  
Np Hardness

AbstractQuasiperiodicity in strings was introduced almost 30 years ago as an extension of string periodicity. The basic notions of quasiperiodicity are cover and seed. A cover of a text T is a string whose occurrences in T cover all positions of T. A seed of text T is a cover of a superstring of T. In various applications exact quasiperiodicity is still not sufficient due to the presence of errors. We consider approximate notions of quasiperiodicity, for which we allow approximate occurrences in T with a small Hamming, Levenshtein or weighted edit distance. In previous work Sim et al. (J Korea Inf Sci Soc 29(1):16–21, 2002) and Christodoulakis et al. (J Autom Lang Comb 10(5/6), 609–626, 2005) showed that computing approximate covers and seeds, respectively, under weighted edit distance is NP-hard. They, therefore, considered restricted approximate covers and seeds which need to be factors of the original string T and presented polynomial-time algorithms for computing them. Further algorithms, considering approximate occurrences with Hamming distance bounded by k, were given in several contributions by Guth et al. They also studied relaxed approximate quasiperiods. We present more efficient algorithms for computing restricted approximate covers and seeds. In particular, we improve upon the complexities of many of the aforementioned algorithms, also for relaxed quasiperiods. Our solutions are especially efficient if the number (or total cost) of allowed errors is small. We also show conditional lower bounds for computing restricted approximate covers and prove NP-hardness of computing non-restricted approximate covers and seeds under the Hamming distance.

Linear Time Optimal Approaches for Max-Profit Inverse 1-Median Location Problems

2018 ◽  
Vol 35 (05) ◽  
pp. 1850030 ◽  
Author(s):  
Esmaeil Afrashteh ◽  
Behrooz Alizadeh ◽  
Fahimeh Baroughi ◽  
Kien Trung Nguyen
Keyword(s):  
Facility Location ◽  
Location Problem ◽  
Linear Time ◽  
Location Problems ◽  
Tree Networks ◽  
New Variant ◽  
Time Optimal ◽  
Total Profit

This paper is concerned with a new variant of the inverse 1-median location problem in which the aim is to modify the customer weights such that a predetermined facility location becomes a 1-median location and the total profit obtained via the weight improvements is maximized. We develop novel combinatorial approaches with linear time complexities for solving the problem on tree networks and in the plane under the rectilinear and Chebyshev norms.

Hybrid ant colony optimization for capacitated multiple-allocation cluster hub location problem

2017 ◽  
Vol 32 (1) ◽  
pp. 44-58 ◽  
Author(s):  
Mohammad Mirabi ◽  
Parya Seddighi
Keyword(s):  
Ant Colony Optimization ◽  
Location Problem ◽  
Demand Management ◽  
Telecommunication Networks ◽  
Ant Colony ◽  
Hub Location ◽  
Hub Location Problem ◽  
Total Cost ◽  
Wide Range ◽  
Cost Of Transportation

AbstractThe hub location problems involve locating facilities and designing hub networks to minimize the total cost of transportation (as a function of distance) between hubs, establishing facilities and demand management. In this paper, we consider the capacitated cluster hub location problem because of its wide range of applications in real-world cases, especially in transportation and telecommunication networks. In this regard, a mathematical model is presented to address this problem under capacity constraints imposed on hubs and transportation lines. Then, a new hybrid algorithm based on simulated annealing and ant colony optimization is proposed to solve the presented problem. Finally, the computational experiments demonstrate that the proposed heuristic algorithm is both effective and efficient.

scholarly journals A SOLUTION ALGORITHM FOR p-MEDIAN LOCATION PROBLEM ON UNCERTAIN RANDOM NETWORKS

2020 ◽  
Vol 35 (1) ◽  
pp. 055
Author(s):  
Akram Soltanpour ◽  
Fahimeh Baroughi ◽  
Behrooz Alizadeh
Keyword(s):  
Optimization Model ◽  
Location Problem ◽  
Random Network ◽  
Solution Algorithm ◽  
Random Networks ◽  
Median Problem ◽  
Chance Theory ◽  
Numerical Example ◽  
Model Based ◽  
Uncertain Random Network

This paper investigatesthe classical $p$-median location problem in a network in which some of the vertex weights and the distances between vertices are uncertain and while others are random. For solving the $p$-median problem in an uncertain random network, an optimization model based on the chance theory is proposed first and then an algorithm is presented to find the $p$-median. Finally, a numerical example is given to illustrate the efficiency of the proposed method

scholarly journals Internet shopping optimization problem

2010 ◽  
Vol 20 (2) ◽  
pp. 385-390 ◽  
Author(s):  
JACEK B£A ZÿEWICZ ◽  
Mikhail Kovalyov ◽  
Jędrzej Musiał ◽  
Andrzej Urbanski ◽  
Adam Wojciechowski
Keyword(s):  
Polynomial Time ◽  
Optimization Problem ◽  
Partial Solution ◽  
The Internet ◽  
Internet Shopping ◽  
Single Product ◽  
Polynomial Time Algorithms ◽  
Special Cases ◽  
Multiple Item ◽  
Np Hardness

Internet shopping optimization problemA high number of Internet shops makes it difficult for a customer to review manually all the available offers and select optimal outlets for shopping. A partial solution to the problem is brought by price comparators which produce price rankings from collected offers. However, their possibilities are limited to a comparison of offers for a single product requested by the customer. The issue we investigate in this paper is a multiple-item multiple-shop optimization problem, in which total expenses of a customer to buy a given set of items should be minimized over all available offers. In this paper, the Internet Shopping Optimization Problem (ISOP) is defined in a formal way and a proof of its strong NP-hardness is provided. We also describe polynomial time algorithms for special cases of the problem.

A DIVIDE-AND-CONQUER ALGORITHM FOR FINDING A MOST RELIABLE SOURCE ON A RING-EMBEDDED TREE NETWORK WITH UNRELIABLE EDGES

2011 ◽  
Vol 03 (04) ◽  
pp. 503-516 ◽  
Author(s):  
WEI DING ◽  
GUOLIANG XUE
Keyword(s):  
Linear Time ◽  
Divide And Conquer ◽  
Tree Networks ◽  
Tree Network ◽  
Divide And Conquer Algorithm ◽  
Failure Tolerance ◽  
Reliable Source ◽  
Binary Division ◽  
General Graphs ◽  
Operational Probability

Given an unreliable communication network, we seek a most reliable source (MRS) of the network, which maximizes the expected number of nodes that are reachable from it. The problem of computing an MRS in general graphs is #P-hard. However, this problem in tree networks has been solved in a linear time. A tree network has a weakness of low capability of failure tolerance. Embedding rings into it by adding some additional certain edges to it can enhance its failure tolerance, resulting in another class of sparse networks, called the ring-tree networks. This class of network also has an underlying tree-like topology, leading to its advantage of being easily administrated. This paper concerns with an important case whose underlying topology is a strip graph, called λ–rings network, and focuses on an unreliable λ–rings network where each link has an independent operational probability while all nodes are immune to failures. We apply the Divide-and-Conquer approach to design a fast algorithm for computing an MRS, and employ a binary division tree (BDT) to analyze its time complexity to be [Formula: see text].

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