Approximating the maximum quadratic assignment problem
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
An algebraic algorithm for weighted linear matroid intersection
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
A hybrid GRASP/VND heuristic for the one-commodity pickup-and-delivery traveling salesman problem
Computers and Operations Research
Genetic algorithm for the one-commodity pickup-and-delivery traveling salesman problem
Computers and Industrial Engineering
Heuristics for the mixed swapping problem
Computers and Operations Research
Dynamic vehicle routing with moving demands: part i: low speed demands and high arrival rates
ACC'09 Proceedings of the 2009 conference on American Control Conference
Understanding planning tasks: domain complexity and heuristic decomposition
Understanding planning tasks: domain complexity and heuristic decomposition
A branch-and-cut algorithm for solving the Non-Preemptive Capacitated Swapping Problem
Discrete Applied Mathematics
The capacitated traveling salesman problem with pickups and deliveries on a tree
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Improved approximation algorithms for metric maximum ATSP and maximum 3-cycle cover problems
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
Improved approximation algorithms for metric maximum ATSP and maximum 3-cycle cover problems
Operations Research Letters
Approximation algorithms for maximum latency and partial cycle cover
Discrete Optimization
Approximation algorithms for the black and white traveling salesman problem
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
The uncapacitated swapping problem on a line and on a circle
Discrete Applied Mathematics
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We provide approximation algorithms for some capacitated vehicle routing and delivery problems. These problems can all be viewed as instances of the following k-delivery TSP: given n source points and n sink points in a metric space, with exactly one item at each source, find a minimum length tour by a vehicle of finite capacity k to pick up and deliver exactly one item to each sink. The only known approximation algorithm for this family of problems is the 2.5-approximation algorithm of Anily and Hassin [ Networks, 22 (1992), pp. 419--433] for the special case k=1. For this case, we use matroid intersection to obtain a 2-approximation algorithm. Based on this algorithm and some additional lower bound arguments, we devise a factor-approximation for k-delivery TSP with arbitrary finite k. We also present a 2-approximation algorithm for the case $k = \infty$.We then initiate the study of dynamic variants of k-delivery TSP that model problems in industrial robotics and other applications. Specifically, we consider the situation where a robot arm (with finite or infinite capacity) must collect n point-objects moving in the Euclidean plane, and deliver them to the origin. The point-objects are moving in the plane with known, identical velocities---they might, for instance, be on a moving conveyor belt. We derive several useful structural properties that lead to constant-factor approximations for problems of this type that are relevant to the robotics application. Along the way, we show that maximum latency TSP is implicit in the dynamic problems, and that the natural "farthest neighbor" heuristic produces a good approximation for several notions of latency.