9,495 research outputs found
An Improved Algorithm for Fixed-Hub Single Allocation Problem
This paper discusses the fixed-hub single allocation problem (FHSAP). In this
problem, a network consists of hub nodes and terminal nodes. Hubs are fixed and
fully connected; each terminal node is connected to a single hub which routes
all its traffic. The goal is to minimize the cost of routing the traffic in the
network. In this paper, we propose a linear programming (LP)-based rounding
algorithm. The algorithm is based on two ideas. First, we modify the LP
relaxation formulation introduced in Ernst and Krishnamoorthy (1996, 1999) by
incorporating a set of validity constraints. Then, after obtaining a fractional
solution to the LP relaxation, we make use of a geometric rounding algorithm to
obtain an integral solution. We show that by incorporating the validity
constraints, the strengthened LP often provides much tighter upper bounds than
the previous methods with a little more computational effort, and the solution
obtained often has a much smaller gap with the optimal solution. We also
formulate a robust version of the FHSAP and show that it can guard against data
uncertainty with little cost
Swap-Robust and Almost Supermagic Complete Graphs for Dynamical Distributed Storage
To prevent service time bottlenecks in distributed storage systems, the
access balancing problem has been studied by designing almost supermagic edge
labelings of certain graphs to balance the access requests to different
servers. In this paper, we introduce the concept of robustness of edge
labelings under limited-magnitude swaps, which is important for studying the
dynamical access balancing problem with respect to changes in data popularity.
We provide upper and lower bounds on the robustness ratio for complete graphs
with vertices, and construct -almost supermagic labelings that are
asymptotically optimal in terms of the robustness ratio.Comment: 27 pages, no figur
Separating hash families with large universe
Separating hash families are useful combinatorial structures which generalize
several well-studied objects in cryptography and coding theory. Let
denote the maximum size of universe for a -perfect hash family of length
over an alphabet of size . In this paper, we show that for all , which answers an open problem about separating
hash families raised by Blackburn et al. in 2008 for certain parameters.
Previously, this result was known only for . Our proof is obtained by
establishing the existence of a large set of integers avoiding nontrivial
solutions to a set of correlated linear equations.Comment: 17 pages, no figur
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