In this paper, we study the prize-collecting $k$ -Steiner tree ( xmlns:xlink="http://www.w3.org/1999/xlink">$\mathsf{PC}k\mathsf{ST}$ ) problem. We are given a graph xmlns:xlink="http://www.w3.org/1999/xlink">$G=(V, E)$ and an integer . The is connected undirected. A vertex xmlns:xli...

In a two-stage robust covering problem, one of several possible scenarios will appear tomorrow and require to be covered, but costs are higher tomorrow than today. What should you anticipatorily buy today, so that the worst-case cost (summed over both days) is minimized? We consider the k-robust model where the possible scenarios tomorrow are given by all demand-subsets of size k. In this paper...

The Kauffman-Harary conjecture is a conjecture for Fox’s colorings of alternating knots with prime determinants. We consider a conjecture for Alexander quandle colorings by referring to the Kauffman-Harary conjecture. We prove that this new conjecture is true for twist knots.

13. Chiasson, J-L. & Cherrington, A. D. (1983) in Glucagon I , (Lefebvre, P. ed.), pp. 361-382, Springer-Verlag, Berlin 14. Frizzell, R. T., Hendrick, G . K., Biggers, D. W., Lacy, D. B., Donahue, D. P., Green, D. R., Carr, R. K., Williams, P. E., Stevenson, R. W. & Cherrington, A. D. (1987) Gluconeogenesis plays the major role in sustaining glucose production during hypoglycemia in response to...

Strictly Chordality-k graphs (SCk) are graphs which are either cycle-free or every induced cycle is of length exactly k, k ≥ 3. Strictly chordality-3 and strictly chordality-4 graphs are well known chordal and chordal bipartite graphs, respectively. For k ≥ 5, the study has been recently initiated in [1] and various structural and algorithmic results are reported. In this paper, we show that ma...

Given a metric space on n points, an α-approximate universal algorithm for the Steiner tree problem outputs a distribution over rooted spanning trees such that for any subset X of vertices containing the root, the expected cost of the induced subtree is within an α factor of the optimal Steiner tree cost for X. An α-approximate differentially private algorithm for the Steiner tree problem takes...

We propose a new algorithm that solves the Steiner tree problem on graphs with vertex set V to optimality in O(B tw+2 · tw · |V |) time, where tw is the graph’s treewidth and the Bell number Bk is the number of partitions of a k-element set. This is a linear time algorithm for graphs with fixed treewidth and a polynomial algorithm for tw = O(log |V |/ log log |V |). While being faster than the ...