J. T. Current and D. A. Schilling. The covering salesman problem. Transportation Science, 23:208-- 213, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....to obtain results for BCCMED with metric c cost. However, our results apply without this restriction and give a slightly better approximation guarantee. 4 Past Work and Relationship with Other Problems In the past, several service constrained minimum cost network problems have been considered in [1, 8, 17, 22, 21]. These papers consider the variant that prescribes a budget on the service distance for each node. The goal is to determine a solution subgraph (which in some of the cited papers is a salesperson tour and in others is a subtree) subject to the budget constraints of the vertices not in the ....

J. T. Current and D. A. Schilling. The covering salesman problem. Transportation Science, 23:208-- 213, 1989.

....algorithm from [20] we get a (1 ; 2(1 1= O(log 3 m log log m) approximation for BCCMED. Our algorithm given in Section 6 uses the techniques from [20] directly and improves this result. 3.2. Related Work. Other service constrained minimum cost network problems have been considered in [1, 6, 12, 16, 17]. These papers consider the variant that prescribes a budget on the service distance for each node not in the tree. The goal is to find a minimum length salesperson tour (or a tree as may be the case) so that all the (customer) nodes are strictly serviced. Restrictions of the problems to geometric ....

J. T. Current and D. A. Schilling, The covering salesman problem, Transportation Science 23 (1989), 208--213.

....we can no longer balance factors between the routes. However, the two criteria which are of interest in this phase are the total length of the bus routes and the total student walking distance to their bus stops. The solution procedure for this phase is a combination of the COVTOUR heuristic of Current and Schilling (1989) and the insertion heuristic of Yurtsever (1988) Here again we use the weighting method to form a single objective function. If both criteria are measure in the same units, for example kilometres, then there is no need to standardize these measures as there was in the districting algorithm. The ....

....each set of bus stops, generate a school bus route on this set of stops. 3. Find the solution from the previous step that has the least total weighted distance and add bus stops to reduce this total distance. Note that the first two steps of this algorithm are the same as the COVTOUR heuristic of Current and Schilling (1989). Each of these three steps is described in more detail below. Find P covering sets of bus stops This step of the algorithm finds a set of bus stops for each route so that every student in a cluster is assigned to a bus stop within the maximum walking distance from their homes. This method is ....

Current, J. and Schilling, D. (1989). The covering salesman problem. Transportation Science, 23:208--213.

....the same type as the customers regions. An alternative is to consider the salesman s initial location as a point region and combine this region with an approximate tour on all other regions using the Combination Lemma. It is interesting to compare our methods to those used by Current and Schilling [CS]. The problem considered in their paper is a graph version of ours: Given a directed graph, non negative costs associated with each arc, and a constant S, find a tour of minimum length such that all nodes not in the tour are at distance at most S from some node in the tour. Their heuristic ....

Current, J.T., and D.A. Schilling (1989), "The Covering Salesman Problem", Transportation science 23, 208-213.

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