Exact Algorithms for B-Bandwidth Problem with Restricted B

The B-BANDWIDTH problem is a decision problem whether the bandwidth of a given graph is smaller than B, and it is NP-complete even if the graph is a small graph class of trees. Cygan and Pilipczuk proposed exponential time and space algorithms for B-BANDWIDTH with n/3 ≤ B where n is the number of vertices. In this paper, we propose two algorithms for the B-BANDWIDTH problem with n/4 ≤ B < n/3. These algorithms are extension of Cygan and Pilipczuk algorithms with restricted B. One of the algorithms takes O∗(4.5n) time and O∗(1.5n) space when n/4 ≤ B < n / 2 log2 1.5, and the other takes O∗(4.77n) time and O∗(1.59n) space when n / 2 log2 1.5 ≤ B < n/3. Our algorithms are fastest O∗(2n) space algorithms for n/4 ≤B < n/3.The 17th Korea-Japan Joint Workshop on Algorithms and Computation, July 13-15, 2014, Okinawa, Japa

An Optimal Algorithm for Finding a Maximum Independent Set of a Circular-Arc Graph.

A new algorithm is presented for finding a maximum independent set of a circular-arc graph. When the graph is given in the form of a family of n arcs, our algorithm requires only O(n log n) time and O(n) space. Furthermore, if the endpoints of the arcs are already sorted, it runs in O(n) time. This algorithm is time- and space-optimal to within a constant factor

The Via Minimization Problem is NP-Complete.

Vias between different layers of interconnection on dense integrated circuits tend to reduce yield, degrade performance, and take up a large amount of chip area. Similarly, contact holes on multilayer printed circuit boards add to manufacturing cost, and reduce reliability. Thus, many researchers have examined ways to minimize the number of vias required for a particular circuit layout. In this paper, we analyze the computational complexity of the so-called Constrained Via Minimization problem. Given an already routed circuit, the problem is to find a minimum cardinality set of vias for which a valid layer assignment exists. We first prove that the corresponding decision problem is NP-complete. We then show that it remains NP-complete even if one or more of the following restrictions are imposed