5145089
A faster off-line algorithm for the TCP acknowledgement problem
In a recent paper [Proceedings of STOC'98, 1998, pp. 389-398], Dooly, Goldman and Scott study a problem that is motivated by the networking problem of dynamically adjusting delays of acknowledgements in the Transmission Control Protocol (TCP). Among other results, they give an O(n2) off-line algorithm for computing the optimal way of acknowledging n packet arrivals and departures.In this brief note, we observe that there is a faster off-line algorithm for this problem with time complexity O(n).
43889321
It is tough to be a plumber
In the Linux computer game KPlumber, the objective is to rotate tiles in a raster of squares so as to complete a system of pipes. We give a complexity classification for the original game and various special cases of it that arise from restricting the set of six possible tiles.Most of the cases are NP-complete. One polynomially solvable case is settled by formulating it as a perfect matching problem; other polynomial cases are settled by simple sweepline techniques. Moreover, we show that all the unsettled cases are polynomial time equivalent.
22610152
Counting k-Subsets and Convex k-gons in the Plane
We consider problems of the following type: Let S be a set of n points in the plane, let p be some point in S and let K be an integer, 3≤k≤n. We show how to compute the overall number of convex k-gons with corners at points in S, for any fixed k≥4.
15492927
Counting Convex Polygons in Planar Point Sets
Given a set S of n points in the plane, we compute in time O(n3) the total number of convex polygons whose vertices are a subset of S. We give an O(m · n3) algorithm for computing the number of convex k-gons with vertices in S, for all values k = 3,…, m; previously known bounds were exponential (O(nk/2). We also compute the number of empty convex polygons (resp.,k-gons, k m) with vertices in S in time O(n3) (resp., O(m · n3)).
29745112
A note on the bottleneck graph partition problem
11379371
Partitioning Graphs into Two Trees
28023212
The Steiner Tree Problem in Kalmanson Matrices and in Circulant Matrices
AbstractWe investigate the computational complexity of two special cases of the Steiner tree problem where the distance matrix is a Kalmanson matrix or a circulant matrix, respectively. For Kalmanson matrices we develop an efficient polynomial time algorithm that is based on dynamic programming. For circulant matrices we give an 
$$\mathcal{N}\mathcal{P}$$
-hardness proof and thus establish computational intractability.
14343122
Backbone Colorings for Networks
We study backbone colorings, a variation on classical vertex colorings: Given a graph G=(V,E) and a spanning subgraph H (the backbone) of G, a backbone coloring for G and H is a proper vertex coloring V →{ 1,2,... } in which the colors assigned to adjacent vertices in H differ by at least two. We concentrate on the cases where the backbone is either a spanning tree or a spanning path.