16833982
The k-level facility location game
We propose a cost-sharing scheme for the k-level facility location game that is cross-monotonic, competitive, and 6-approximate cost recovery. This extends the recent result for the 1-level facility location game of Pal and Tardos.
35793386
An improved algorithm for decomposing arc flows into multipath flows
We consider a multipath maximum flow problem introduced by Kishimoto (Networks 27(4)(1996)279-291). The focus is on efficient transformation from arc flows into multipath flows, where a multipath flow is a nonnegative combination of multipaths. A new algorithm that is more efficient than existing ones is proposed for the transformation.
33293485
The k-Steiner Ratio in Graphs
A Steiner minimum tree (SMT) is the shortest-length tree in a metric space interconnecting a set of points, called the regular points, possibly using additional vertices. A k-size Steiner minimum tree (kSMT) is one that can be split into components where all regular points are leaves and all components have at most k leaves. The k-Steiner ratio, $\rho_{k}$, is the infimum of the ratios SMT/kSMT over all finite sets of regular points in all possible metric spaces, where the distances are given by a complete graph. Previously, only $\rho_{2}$ and $\rho_{3}$ were known exactly in graphs, and some bounds were known for other values of k. In this paper, we determine $\rho_{k}$ exactly for all k. From this we prove a better approximation ratio for the Steiner tree problem in graphs.
20341554
On greedy heuristics for steiner minimum trees
We disprove a conjecture of Shor and Smith on a greedy heuristic for the Steiner minimum tree by showing that the length ratio between the Steiner minimum tree and the greedy tree constructed by their method for the same set of points can be arbitrarily close to√3/2. We also propose a new conjecture.
14358235
New bounds on a hypercube coloring problem
In studying the scalability of optical networks, one problem which arises involves coloring the vertices of the n-cube with as few colors as possible such that any two vertices whose Hamming distance is at most k are colored differently. Determining the exact value of χ??(n), the minimum number of colors needed, appears to be a difficult problem. In this note, we improve the known lower and upper bounds of χ??(n) and indicate the connection of this coloring problem to linear codes.
2477251
PCR-assist CBR for delivering pre-recorded MPEG-2 transport streams
Transmitting compressed variable bit-rate (VBR) video with a traditional constant bit-rate (CBR) service for continuous playback requires a large buffer on the viewer's side. In this paper, we study a new CBR transmission scheme which employs the program clock references (PCR) that are embedded in the MPEG-2 transport streams to reduce the buffer requirement. The scheme is called "PCR-assist CBR" (PCBR). The PCBR scheme uses PCRs to examine its transmission regularly. It holds up the transmission if it is ahead of schedule. Based on experimental results with video traces, the PCBR scheme reduces the buffer requirement at the cost of a higher transmission rate.
10138476
Matroids and Subset Interconnection Design
A problem arising in the design of vacuum systems and having applications to some natural problems of interconnection design is described as follows. (1) Given a set X and subsets $X_i ,Y_i $ of $X,i = 1, \cdots ,n$, satisfying $X_i \cap Y_i = \O $, find a graph G with vertex set X and the minimum number of edges such that for any i, the subgraph induced by $X\backslash Y_i $ has a connected component containing $X_i $.Two other problems related to this one are the following ones. (2) Given a set X and subsets $X_1 ,X_2 , \cdots ,X_n $ such that $X = \cup _{i = 1}^n X_i $, find a graph G with vertex set X and the minimum number of edges such that for any i the subgraph $G_i $ induced by $X_i $ in G is connected. (3) Given a set X and subsets $X_1 ,X_2 , \cdots ,X_n $ such that $X = \cup _{i = 1}^n X_i $, find a graph G with vertex set X, find a graph G with vertex set X and the minimum number of edges such that for any subset I of $\{ 1, \cdots ,n \}$, the subgraph induced by $ \cap _{i \in I} X_i $ is co...