C. H. Papadimitriou. On the complexity of edge traversing. J. ACM, 23(3):544--554, 1976.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....is not true. The chinese postman problem (cpp) in mixed graphs is a variant of mccp: given a strongly connected mixed graph M , nd a postman walk in M of minimum length. We know that cpp can be solved in polynomial time in graphs [8] and in digraphs [9] On the other hand, Papadimitriou [13] proved that cpp is NP hard on planar mixed graphs. In this paper, we study the complexity of mccp and cpp on mixed graphs with a certain connectivity parameter tree width bounded by a constant. The tree width of a graph G is de ned on top of a tree decomposition of G. The study of ....

C.H. Papadimitriou, On the complexity of edge traversing, Journal of ACM, 23 (1976), 544-554.

....a shortest tour of a strongly connected graph under the restriction that each edge and arc must be traversed at least once. For an arbitrary mixed graph with nonnegative costs, it can be checked in polynomial time whether the graph has a tour in which each edge and arc is traversed exactly once [3, 8]. The special case in which the underlying graph is completely undirected (i.e. consists entirely of two way streets) has been examined in detail and can be solved efficiently [6, 1] The special case in which the network consists entirely of directed edges can also be solved in polynomial time ....

.... in detail and can be solved efficiently [6, 1] The special case in which the network consists entirely of directed edges can also be solved in polynomial time [2] The mixed Chinese postman problem, in which the graph consists of both directed and undirected edges is known to be NP complete [8]. In [5] Kappauf and Koehler formulated the mixed Chinese postman problem as an integer linear program and research partially supported by an NSF PYI award CCR 89 96272 with matching support from UPS, and Sun Microsystems, and by the National Science Foundation, the Air Force Office of Scientific ....

Papadimitriou, C.H. On the Complexity of Edge Traversing. J. of the Assoc. of Comptng. Machinery 23 (1976), 544-554.

....we are asked to find a shortest tour visiting all edges (of length 1) of G. This problem is known as the Chinese Postman Problem [5] It has polynomial time solutions for undirected graphs and directed graphs [3] but it is NP complete on mixed graphs with both undirected and directed edges [7]. Theorem 1. On undirected graphs, no online algorithm can be better than 2 competitive, and DFS achieves this bound. Proof. Assume G is a triangle where each of the three nodes has a self loop attached. The algorithm is given one of the nodes as the start node s, and it just sees 4 outgoing ....

C. H. Papadimitriou. On the complexity of edge traversing. Journal of the ACM, 23(3):544--554, 1976. 6

....pick up, and snow removal can be modeled by CPP. CPP can be solved in polynomial time if all edges of the graph are undirected, or if all edges are directed. However, if the input graph is mixed, i.e. if it contains both undirected and directed edges, CPP was shown to be NP hard by Papadimitriou [12]. The Mixed Postman Problem (MPP) is a generalization of CPP, and it enables us to model one way and two way streets. A preliminary version of the paper appeared in SODA 1999 [15] y Department of Computer Science, The University of Texas at Dallas, Richardson, TX 75083 0688. Research ....

C. H. Papadimitriou. On the complexity of edge traversing. J. Assoc. Comput. Mach., 23:544{ 554, 1976.

....must cover the same city with their routes. The Chinese Postman Problem can be solved by a polynomial time algorithm if the graph is either undirected or directed [8] The Chinese Postman problem for a mixed graph that has undirected and directed edges was shown to be NP complete by Papadimitriou [9]. We do not know an optimal off line algorithm for the Weak Postman Problem; this may be an NP hard problem. This is an interesting open problem. We now give an approximation algorithm for the off line piecemeal search problem using a simple interrupted DFS approach. Theorem 1 There exists an ....

Papadimitriou, Christos H. "On the complexity of edge traversing" J. Assoc. Comp. Mach., 1976, volume 23, pp. 544--554. PIECEMEAL LEARNING OF AN UNKNOWN ENVIRONMENT 29

....TX 75083 0688. Research supported by NSF Research Initiation Award CCR 9409625. Email: rbk utdallas.edu. y Department of Computer Science, The University of Texas at Dallas, and Samsung Telecommunications America, Inc. Email: veerasam utdallas.edu. polynomially solvable, Papadimitriou [13] showed that MPP is NP hard. There are other related problems, such as the Rural postman problem and the Windy postman problem, which are also NP hard [4, 5] Many practical applications like mail delivery, snow removal, and trash pick up can be modeled as instances of MPP, and hence it is ....

C. H. Papadimitriou. On the complexity of edge traversing. J. Assoc. Comput. Mach., 23:544-- 554, 1976.

....can also be used for circulation problems. As special cases, we present algorithms for covering paths and postman tour problems. For example, we obtain an O(n(m n log n) log(m n) algorithm for the Chinese postman problem. For this problem, the best previously published algorithm was O(n 5 ) [Papadimitriou, 1976], and an O(mn log n) algorithm can be obtained by reducing the problem to a minimum cost flow problem using balancing and solving the reduced problem by scaling [Gabow and Tarjan, 1987] Our algorithm is faster than either of these methods. Several versions of the covering paths problems and the ....

....Problems X i ( j) are NP complete, where X = C , F , CP , PT , i = 2 , 3, and j = 0 , 1 , 2. Proof. We first note that Problem PT 3 (2) can be reduced to Problems CP 3 (2) and CP 2 (2) and that Problem CP 2 (2) can be reduced to Problem PT 2 (2) Since Problem PT 3 (2) is NP complete [Papadimitriou, 1976], all of them are. The reduction is the same as that in the proof of Theorem 8.1, and we omit the details. Since Problems F i (2) C i (2) and CP i (2) PT i (2) are equivalent, they are special cases of Problems X i (1) which in turn are special cases of Problems X i (0) ....

Papadimitriou, C. H. [1976]. On the complexity of edge traversing, J. ACM 23:3, 544-554.

....must cover the same city with their routes. The Chinese Postman Problem can be solved by a polynomial time algorithm if the graph is either undirected or directed [9] The Chinese Postman problem for a mixed graph that has undirected and directed edges was shown to be NP complete by Papadimitriou [10]. We do not know an optimal off line algorithm for the Weak Postman Problem; this may be an NP hard problem. This is an interesting open problem. We now give an approximation algorithm for the off line piecemeal search problem using a simple interrupted DFS approach. Theorem 1 There exists an ....

Papadimitriou, Christos H. "On the complexity of edge traversing" J. Assoc. Comp. Mach., 1976, volume 23, pp. 544--554.

....exists a unique postman walk of length l = n Gamma k 1 in G. Finding the minimum postman walk is known as the Chinese postman problem [17] Polynomial algorithms based on bipartite matching exist for directed and undirected graphs, 7] although the problem is NP complete for mixed graphs [22]. For a digraph G, there may exist positive integers l such that a postman walk of length l either (1) does not exist, 2) exists and is unique, or (3) exists and non unique. For example, the graph in Figure 1, 1) does not have a postman walk of length w x y z 6a b 1, 2) has a unique ....

C. Papadimitriou. The complexity of edge traversing. J. ACM, 23:544--554, 1976.

....tour of a given graph G such that each edge of G is traversed at least once. This problem is motivated by the problem faced by a postman who must deliver mail along each edge of a graph and return to his starting point. This problem has many kinds of variations and has been extensively studied [2, 3, 4, 5, 7, 8, 12, 13, 14, 15, 16, 18, 20, 21]. We consider in this paper the following situation: A postman must do a side job while delivering mail. A side job is given as a series of actions, and each edge is assigned an action which the postman must take when he traverses the edge. Therefore, it is needed for the postman to test if a ....

C. H. Papadimitriou. On the complexity of edge traversing. J. Assoc. Comput. Mach., 23:544--554, 1976.

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C. H. Papadimitriou. On the complexity of edge traversing. J. ACM, 23(3):544--554, 1976.

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