Shift-and-merge technique for the DP solution of the time-constrained backpacker problem

Authors:
Byungjun You;Takeo Yamada
Affiliations:
Department of Computer Science, The National Defense Academy, Yokosuka, Kanagawa 239-8686, Japan;Department of Computer Science, The National Defense Academy, Yokosuka, Kanagawa 239-8686, Japan
Venue:
Computers and Operations Research
Year:
2012

Citing 11
Cited 0

Knapsack problems: algorithms and computer implementations

Knapsack problems: algorithms and computer implementations
Network flows: theory, algorithms, and applications

Network flows: theory, algorithms, and applications
Computing Partitions with Applications to the Knapsack Problem

Journal of the ACM (JACM)
Heuristic and exact algorithms for the precedence-constrained knapsack problem

Journal of Optimization Theory and Applications
Algorithms in C

Algorithms in C
Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness
Introduction to Algorithms

Introduction to Algorithms
The Effects of Coefficient Correlation Structure in Two-Dimensional Knapsack Problems on Solution Procedure Performance

Management Science
An Exact Algorithm for the Two-Constraint 0--1 Knapsack Problem

Operations Research
Load balancing methods and parallel dynamic programming algorithm using dominance technique applied to the 0--1 knapsack problem

Journal of Parallel and Distributed Computing
Lagrangean heuristics combined with reoptimization for the 0-1 bidimensional knapsack problem

Discrete Applied Mathematics - Special issue: International symposium on combinatorial optimization CO'02

Quantified Score

Hi-index	0.02

Visualization

Abstract

We formulate the time-constrained backpacker problem as an extension of the classical knapsack problem (KP), where a 'backpacker' travels from a origin to a destination on a directed acyclic graph, and collects items en route within the capacity of his knapsack and within a fixed time limit. We present a dynamic programming (DP) algorithm to solve this problem to optimality, and a 'shift-and-merge' DP algorithm to solve larger instances. The latter is an extension of the list-type DP, which has been successful for one-dimensional KPs, to the two-dimensional case. Computational experiments on a series of instances demonstrate advantage of the shift-and-merge technique over commercial MIP solvers.