Showing papers by "Center for Discrete Mathematics and Theoretical Computer Science published in 2011"
TL;DR: The Dynamic Programming algorithm COMBO is used to solve KP and the branch and bound method EXPKNAP is modified for KP to solve the PKP, which is similar to the traditional knapsack problem except that the profits of items may be non-positive, and the weight sum has two sided limits on capacity.
Abstract: The 0---1 linear knapsack problem with a single continuous variable (KPC) is an extension of the binary knapsack problem (KP). It is an NP-hard problem. In this paper, we show that KPC can be reduced to KP and a pseudo-knapsack problem (PKP), which is similar to the traditional knapsack problem except that the profits of items may be non-positive, and the weight sum has two sided limits on capacity. We use the Dynamic Programming algorithm COMBO (Martello et al., Manag Sci 45(3):414---424, 1999) to solve KP, and modify the branch and bound method EXPKNAP (Pisinger, Eur J Oper Res 87:175---187, 1995) for KP to solve the PKP. Numerical experiments show the efficiency of our method.
15 citations
TL;DR: A penalty based method to convert the problem into an unconstrained one, and then use the above method to solve the later problem to show the effectiveness of the proposed algorithm.
10 citations
18 Nov 2011
TL;DR: It is come to a conclusion that the minimum parallel clique cover of $CCG$ is equivalent to the optimal solution of 2-layer manhattan channel routing where vertical constrains are noncyclic and extra empty columns and doglegs are not allowed.
Abstract: Channel routing is a key problem in the area of VLSI layout. Finding a minimum width solution of channel routing was proved to be NP-hard by Szymanski. In this paper, we come to a conclusion that the minimum parallel clique cover of $CCG$ is equivalent to the optimal solution of 2-layer manhattan channel routing where vertical constrains are noncyclic and extra empty columns and doglegs are not allowed. We also gave a new heuristic algorithm based on the conclusion to solve the problem of 2-layer manhattan channel routing.
1 citations
01 Dec 2011
TL;DR: It is proved that the symmetrical routing problem under the H-V model is equivalent to finding a Steiner free of the corresponding vertices for all of the pins in the valid connected graph.
Abstract: In the integrated circuit routing, we often consider the routing for some special nets under the restrictions, such as equidistance and symmetry The symmetrical routing is operated between the routing for the bus and the clock and the routing for most the others without the priority We prove that the symmetrical routing problem under the H-V model is equivalent to finding a Steiner free of the corresponding vertices for all of the pins in the valid connected graph We put forward an algorithm for the symmetrical routing under the H-V model In the actual wiring process, when the symmetrical routing is needed, the routing is finished by hand This paper provides a method and the theory based on graphs for the automation design of the symmetrical routing
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TL;DR: This paper generalizes Opsut's result to the competition numbers of generalized line graphs, that is, it is shown that the competition number of a generalized line graph is at most two, and give necessary conditions and sufficient con ditions for the competitionNumber of a normalized line graph being one.
Abstract: In 1982, Opsut showed that the competition number of a line graph is at most two and gave a necessary and sufficient condition for the competition number of a line graph being one. In this note, we generalize this result to the competition numbers of generalized line graphs, that is, we show that the competition number of a generalized line graph is at most two, and give necessary conditions and sufficient conditions for the competition number of a generalized line graph being one.