Remarks on d-Dimensional TSP Optimal Tour Length Behaviour
نویسنده
چکیده
The well-known O ( n1−1/d ) behaviour of the optimal tour length for TSP in d-dimensional Cartesian space causes breaches of the triangle inequality. Other practical inadequacies of this model are discussed, including its use as basis for approximation of the TSP optimal tour length or bounds derivations, which I attempt to remedy.
منابع مشابه
The Euclidean Traveling Salesman Problem and a Space-filling Curve
We elucidate the relationship between space-llling curves and the Euclidean Traveling 2 Salesman Problem (TSP) by reference to a particular space-lling curve whose scaling behaviour is strongly related to the conjectured scaling behaviour of the optimal TSP tour. We suggest that space-lling curves can be used to generate testbed TSPs: sets of points which in the limit cover a planar surface and...
متن کاملThe Tsp and the Sum of its Marginal Values
This paper introduces a new notion related to the traveling salesperson problem (TSP) — the notion of the TSP ratio. The TSP ratio of a TSP instance I is the sum of the marginal values of the nodes of I divided by the length of the optimal TSP tour on I, where the marginal value of a node i ∈ I is the difference between the length of the optimal tour on I and the length of the optimal tour on I...
متن کاملThe Random Link Approximation for the Euclidean Traveling Salesman Problem
The traveling salesman problem (TSP) consists of finding the length of the shortest closed tour visiting N "cities". We consider the Euclidean TSP where the cities are distributed randomly and independently in a d-dimensional unit hypercube. Working with periodic boundary conditions and inspired by a remarkable universality in the kth nearest neighbor distribution, we find for the average optim...
متن کاملThe Metric TSP and the Sum of its Marginal Values
This paper examines the relation between the length of an optimal Traveling Salesman tour and the sum of its nodes’ marginal values (a node’s marginal value is the difference between the length of an optimal TSP tour over a given node set and the length of an optimal TSP tour over the node set minus the node). To our knowledge, this problem has not been studied previously. We find that in metri...
متن کاملA CONSTRAINED SOLID TSP IN FUZZY ENVIRONMENT: TWO HEURISTIC APPROACHES
A solid travelling salesman problem (STSP) is a travelling salesman problem (TSP) where the salesman visits all the cities only once in his tour using dierent conveyances to travel from one city to another. Costs and environmental eect factors for travelling between the cities using dierent conveyances are dierent. Goal of the problem is to nd a complete tour with minimum cost that damages the ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره cs.CG/0209027 شماره
صفحات -
تاریخ انتشار 2002