1,483 research outputs found
An Efficient Algorithm For Chinese Postman Walk on Bi-directed de Bruijn Graphs
Sequence assembly from short reads is an important problem in biology. It is
known that solving the sequence assembly problem exactly on a bi-directed de
Bruijn graph or a string graph is intractable. However finding a Shortest
Double stranded DNA string (SDDNA) containing all the k-long words in the reads
seems to be a good heuristic to get close to the original genome. This problem
is equivalent to finding a cyclic Chinese Postman (CP) walk on the underlying
un-weighted bi-directed de Bruijn graph built from the reads. The Chinese
Postman walk Problem (CPP) is solved by reducing it to a general bi-directed
flow on this graph which runs in O(|E|2 log2(|V |)) time. In this paper we show
that the cyclic CPP on bi-directed graphs can be solved without reducing it to
bi-directed flow. We present a ?(p(|V | + |E|) log(|V |) + (dmaxp)3) time
algorithm to solve the cyclic CPP on a weighted bi-directed de Bruijn graph,
where p = max{|{v|din(v) - dout(v) > 0}|, |{v|din(v) - dout(v) < 0}|} and dmax
= max{|din(v) - dout(v)}. Our algorithm performs asymptotically better than the
bidirected flow algorithm when the number of imbalanced nodes p is much less
than the nodes in the bi-directed graph. From our experimental results on
various datasets, we have noticed that the value of p/|V | lies between 0.08%
and 0.13% with 95% probability
Efficient Multi-Robot Coverage of a Known Environment
This paper addresses the complete area coverage problem of a known
environment by multiple-robots. Complete area coverage is the problem of moving
an end-effector over all available space while avoiding existing obstacles. In
such tasks, using multiple robots can increase the efficiency of the area
coverage in terms of minimizing the operational time and increase the
robustness in the face of robot attrition. Unfortunately, the problem of
finding an optimal solution for such an area coverage problem with multiple
robots is known to be NP-complete. In this paper we present two approximation
heuristics for solving the multi-robot coverage problem. The first solution
presented is a direct extension of an efficient single robot area coverage
algorithm, based on an exact cellular decomposition. The second algorithm is a
greedy approach that divides the area into equal regions and applies an
efficient single-robot coverage algorithm to each region. We present
experimental results for two algorithms. Results indicate that our approaches
provide good coverage distribution between robots and minimize the workload per
robot, meanwhile ensuring complete coverage of the area.Comment: In proceedings of IEEE/RSJ International Conference on Intelligent
Robots and Systems (IROS), 201
Min-Max K-vehicles Windy Rural Postman Problem
[EN] In this article the Min-Max version of the windy rural postman problem with several vehicles is introduced. For this problem, in which the objective is to minimize the length of the longest tour in order to find a set of balanced tours for the vehicles, we present here an ILP formulation and study its associated polyhedron. Based on its partial description, a branch-and-cut algorithm has been implemented and computational results on a large set of instances are finally presented. (C) 2009 Wiley Periodicals, Inc. NETWORKS, Vol. 54(4),216-226 2009Contract grant sponsor: Ministerio de Education y Ciencia of Spain: Contract gram number: MTM2006-14961-C05-02Benavent López, E.; Corberan, A.; Plana, I.; Sanchís Llopis, JM. (2009). Min-Max K-vehicles Windy Rural Postman Problem. Networks. 54(4):216-226. https://doi.org/10.1002/net.20334S216226544D. Ahr Contributions to multiple postmen problems 2004D. Ahr G. Reinelt “New heuristics and lower bounds for the min-max k -Chinese postman problem” Algorithms-ESA 2002, 10th Annual European Symposium, Rome, Italy, 2002, Lecture Notes in Computer Science 2461 R. Möring R. Raman Springer Berlin 2002 64 74Ahr, D., & Reinelt, G. (2006). A tabu search algorithm for the min–max k-Chinese postman problem. Computers & Operations Research, 33(12), 3403-3422. doi:10.1016/j.cor.2005.02.011D. Applegate R.E. Bixby V. Chvátal W. Cook Finding cuts in the TSP 1995Barahona, F., & Grötschel, M. (1986). On the cycle polytope of a binary matroid. Journal of Combinatorial Theory, Series B, 40(1), 40-62. doi:10.1016/0095-8956(86)90063-8Belenguer, J. M., & Benavent, E. (1998). Computational Optimization and Applications, 10(2), 165-187. doi:10.1023/a:1018316919294Benavent, E., Carrotta, A., Corberán, A., Sanchis, J. M., & Vigo, D. (2007). Lower bounds and heuristics for the Windy Rural Postman Problem. European Journal of Operational Research, 176(2), 855-869. doi:10.1016/j.ejor.2005.09.021N. Christofides V. Campos A. Corberán E. Mota An algorithm for the rural postman problem 1981Christofides, N., Campos, V., Corberán, A., & Mota, E. (1986). An algorithm for the Rural Postman problem on a directed graph. Netflow at Pisa, 155-166. doi:10.1007/bfb0121091Corberán, A., Plana, I., & Sanchis, J. M. (2008). The Windy General Routing Polyhedron: A Global View of Many Known Arc Routing Polyhedra. SIAM Journal on Discrete Mathematics, 22(2), 606-628. doi:10.1137/050640886Corberán, A., Plana, I., & Sanchis, J. M. (2007). A branch & cut algorithm for the windy general routing problem and special cases. Networks, 49(4), 245-257. doi:10.1002/net.20176Eiselt, H. A., Gendreau, M., & Laporte, G. (1995). Arc Routing Problems, Part II: The Rural Postman Problem. Operations Research, 43(3), 399-414. doi:10.1287/opre.43.3.399Frederickson, G. N., Hecht, M. S., & Kim, C. E. (1978). Approximation Algorithms for Some Routing Problems. SIAM Journal on Computing, 7(2), 178-193. doi:10.1137/0207017G. Ghiani D. Laganá G. Laporte R. Musmanno A branch-and-cut algorithm for the undirected capacitated arc routing problem 2007Ghiani, G., & Laporte, G. (2000). A branch-and-cut algorithm for the Undirected Rural Postman Problem. Mathematical Programming, 87(3), 467-481. doi:10.1007/s101070050007Golden, B. L., & Wong, R. T. (1981). Capacitated arc routing problems. Networks, 11(3), 305-315. doi:10.1002/net.3230110308Padberg, M. W., & Rao, M. R. (1982). Odd Minimum Cut-Sets andb-Matchings. Mathematics of Operations Research, 7(1), 67-80. doi:10.1287/moor.7.1.67Pearn, W. L. (1994). Solvable cases of the k-person Chinese postman problem. Operations Research Letters, 16(4), 241-244. doi:10.1016/0167-6377(94)90073-
Parameterized Rural Postman Problem
The Directed Rural Postman Problem (DRPP) can be formulated as follows: given
a strongly connected directed multigraph with nonnegative integral
weights on the arcs, a subset of and a nonnegative integer ,
decide whether has a closed directed walk containing every arc of and
of total weight at most . Let be the number of weakly connected
components in the the subgraph of induced by . Sorge et al. (2012) ask
whether the DRPP is fixed-parameter tractable (FPT) when parameterized by ,
i.e., whether there is an algorithm of running time where is a
function of only and the notation suppresses polynomial factors.
Sorge et al. (2012) note that this question is of significant practical
relevance and has been open for more than thirty years. Using an algebraic
approach, we prove that DRPP has a randomized algorithm of running time
when is bounded by a polynomial in the number of vertices in
. We also show that the same result holds for the undirected version of
DRPP, where is a connected undirected multigraph
New Facets and an Enhanced Branch-and-Cut for the Min-Max K-Windy Rural Postman Problem
[EN] The min-max windy rural postman problem is a multiple vehicle version of the windy rural postman problem, WRPP, which consists of minimizing the length of the longest route to find a set of balanced routes for the vehicles. In a previous paper, an ILP formulation and a partial polyhedral study were presented, and a preliminary branch-and-cut algorithm that produced some promising computational results was implemented. In this article, we present further results for this problem. We describe several new facet-inducing inequalities obtained from the WRPP, as well as some inequalities that have to be satisfied by any optimal solution. We present an enhanced branch-and-cut algorithm that takes advantage of both these new inequalities and high quality min-max K-WRPP feasible solutions obtained by a metaheuristic. Computational results on a large set of instances are also reported. © 2011 Wiley Periodicals, Inc.Contract grant sponsor: Ministerio de Ciencia e Innovacion of Spain; Contract grant numbers: MTM2006-14961-C05-02, MTM2009-14039-C06-02Benavent López, E.; Corberán, A.; Plana, I.; Sanchís Llopis, JM. (2011). New Facets and an Enhanced Branch-and-Cut for the Min-Max K-Windy Rural Postman Problem. Networks. 58(4):255-272. https://doi.org/10.1002/net.20469S255272584D. Ahr Contributions to multiple postmen problems 2004Ahr, D., & Reinelt, G. (2002). New Heuristics and Lower Bounds for the Min-Max k-Chinese Postman Problem. Lecture Notes in Computer Science, 64-74. doi:10.1007/3-540-45749-6_10Ahr, D., & Reinelt, G. (2006). A tabu search algorithm for the min–max k-Chinese postman problem. Computers & Operations Research, 33(12), 3403-3422. doi:10.1016/j.cor.2005.02.011D. Applegate R. E. Bixby V. Chvátal W. Cook Finding cuts in the TSP 1995Benavent, E., Carrotta, A., Corberán, A., Sanchis, J. M., & Vigo, D. (2007). Lower bounds and heuristics for the Windy Rural Postman Problem. European Journal of Operational Research, 176(2), 855-869. doi:10.1016/j.ejor.2005.09.021Benavent, E., Corberán, A., Plana, I., & Sanchis, J. M. (2009). Min-Max K
-vehicles windy rural postman problem. Networks, 54(4), 216-226. doi:10.1002/net.20334Benavent, E., Corberán, Á., & Sanchis, J. M. (2009). A metaheuristic for the min–max windy rural postman problem with K vehicles. Computational Management Science, 7(3), 269-287. doi:10.1007/s10287-009-0119-2Corberáan, A., Letchford, A. N., & Sanchis, J. M. (2001). A cutting plane algorithm for the General Routing Problem. Mathematical Programming, 90(2), 291-316. doi:10.1007/pl00011426Corberán, A., Plana, I., & Sanchis, J. M. (2007). A branch & cut algorithm for the windy general routing problem and special cases. Networks, 49(4), 245-257. doi:10.1002/net.20176Corberán, A., Plana, I., & Sanchis, J. M. (2008). The Windy General Routing Polyhedron: A Global View of Many Known Arc Routing Polyhedra. SIAM Journal on Discrete Mathematics, 22(2), 606-628. doi:10.1137/050640886Frederickson, G. N., Hecht, M. S., & Kim, C. E. (1978). Approximation Algorithms for Some Routing Problems. SIAM Journal on Computing, 7(2), 178-193. doi:10.1137/0207017Pearn, W. L. (1994). Solvable cases of the k-person Chinese postman problem. Operations Research Letters, 16(4), 241-244. doi:10.1016/0167-6377(94)90073-6I. Plana The windy general routing problem 200
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