18860643
The multiroute maximum flow problem revisited
We are given a directed network G = (V, A, u) with vertex setV , arc setA, a source vertexs ∈ V , a destination vertex t ∈ V , a finite capacity vector u = {uij}ij∈A, and a positive integerm ∈ Z+. The multiroute maximum flow problem ( m-MFP) generalizes the ordinary maximum flow problem by seeking a maximum flow from s to t subject to not only the regular flow conservation constraints at the vertices (except s andt) and the flow capacity constraints at the arcs, but also the extra constraints that any flow must be routed alon g m arc-disjoints-t paths. In this paper, we devise two new combinatorial algorithms for m-MFP. One is based on Newton’s method and another is based on augmenting-path technique. We also show how the Newton-based algorithm unifies two existing algorithms, and how the augmen ting-path algorithm is strongly polynomial for case m = 2.
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.
16471624
Preemptive on-line scheduling for two uniform processors
This paper considers the problem of preemptive on-line scheduling for two uniform processors in which one of the processors has speed 1 and the other has speed s>=1. The objective is to minimize the makespan. A best possible algorithm with competitive ratio of (1+s)^2/(1+s+s^2) is proposed for this problem.
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.
9780632
An integrated admission control scheme for the delivery of streaming media
Quality of service (QoS) assurance is a major concern in media-on-demand (MoD) systems. Admission control is one of the most important issues that need to be addressed for QoS assurance. Also, smoothing is a basic technique for the media server to improve its bandwidth and buffer utilization. However, existing approaches cannot achieve the best resource utilization because (1) they cannot fully utilize the time-varying buffer spaces available at both server and client sides due to the separation of admission control and smoothing processes, and (2) the computing time is unacceptable for media of long duration. In this paper, we formulate the admission control as an integer programming problem and propose several heuristic methods for solving the problem. Specially, we introduce an efficient scheme, called batched admission (BA) scheme, which integrates admission control, transmission rate smoothing, and batching, to achieve best resource utilization with guaranteed QoS. Experimental studies show that the BA scheme outperforms existing approaches.
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.
9317964
The Steiner ratio for the dual normed plane
A minimum Steiner tree for a given set X of points is a network interconnecting the points of X having minimal possible total length. The Steiner ratio for a metric space is the largest lower bound for the ratio of lengths between a minimum Steiner tree and a minimum spanning tree on the same set of points in the metric space. Du et al. (1993) conjectured that the Steiner ratio on a normed plane is equal to the Steiner ratio on its dual plane. In this paper we show that this conjecture is true for Ixl ~<5.
42394808
on Component-size Bounded Steiner Trees
A Steiner tree is a tree interconnecting a given set of points in a metric space such that all leaves are given points. A (full) component of a Steiner tree is a subtree which results from splitting the Steiner tree at some given points. A k-size Steiner tree is a Steiner tree in which every component has at most k given points. The k-Steiner ratio is the largest lower bound for the ratio between lengths of a minimum Steiner tree and a minimum k-size Steiner tree for the same set of points. In this paper, we determine the 3-Steiner ratio in weighted graphs.
44914304
Steiner minimal trees on sets of four points
LetS = {A, B, C, D} consist of the four corner points of a convex quadrilateral where diagonals [A, C] and [B, D] intersect at the pointO. There are two possible full Steiner trees forS, theAB-CD tree hasA andB adjacent to one Steiner point, andC andD to another; theAD-BC tree hasA andD adjacent to one Steiner point, andB andC to another. Pollak proved that if both full Steiner trees exist, then theAB-CD (AD-BC) tree is the Steiner minimal tree ifAOD>3 (<) 90°, and both are Steiner minimal trees ifAOD=90°. While the theorem has been crucially used in obtaining results on Steiner minimal trees in general, its applicability is sometimes restricted because of the condition that both full Steiner trees must exist. In this paper we remove this obstacle by showing: (i) Necessary and sufficient conditions for the existence of either full Steiner tree forS. (ii) IfAOD≥90°, then theAB-CD tree is the SMT even if theAD-BC tree does not exist. (iii) IfAOD<90° but theAD-BC tree does not exist, then theAB-CD tree cannot be ruled out as a Steiner minimal tree, though under certain broad conditions it can.
206027538
A coloring problem on the n-cube
Abstract In this paper, we consider a coloring problem on the n-cube that arises in the study of scalability of optical networks. Let χ k (n) be the minimum number of colors needed to color the vertices of the n-cube so that every two vertices with Hamming distance ⩽k have different colors. We show that for k=3, 2n⩽χ 3 (n)⩽2 ⌈ log 2 n⌉+1 . We also provide upper and lower bounds on χ k (n) for general k.