114,501 research outputs found
Max-balanced flows in oriented matroids
Let M=(E,O) be an oriented matroid on the ground set E. A real-valued vector x defined on E is a max-balanced flow for M if for every signed cocircuit Y∈O⊥, we have maxeεY+Xe=maxeεY−Xe. We extend the admissibility and decomposition theorems of Hamacher from regular to general oriented matroids in the case of max-balanced flows, which gives necessary and sufficient conditions for the existence of a max-balanced flow x satisfying l⩽×⩽u. We further investigate the semilattice of such flows under the usual coordinate partial order, and obtain structural results for the minimal elements. We also give necessary and sufficient conditions for the existence of such a flow when we are allowed to reverse the signs on a subset F⊆E. The proofs of all of our results are constructive, and yield polynomial algorithms in case M is coordinatized by a rational matrix A. In this same setting, we describe a polynomial algorithm that for a given vector w defined on E, either finds a potential p such that w′=w+pA is max-balanced, or a certificate that M has no max-balanced flow
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Single-phase mixing through a narrow gap
Mixing through narrow gaps connecting adjacent flow paths is an important mass and heat transfer process for many thermo-hydraulic applications. Such flows are considered balanced when the inlet flow speeds of adjacent subchannels are matched. In the present work, experimental observations are presented for balanced and unbalanced flows including the mixing coefficients and flow visualization within the gap. The large coherent structures are identified, with frequency in general agreement with those reported by previous investigators. To utilize Proper Orthogonal Decomposition (POD) for the discrete data yielded by PIV, we employ method of Singular Value Decomposition (SVD). The bulk of the mixing is attributed to the dominant modes and demonstrate that mixing rates estimated from velocity measurements are in fair agreement with mixing coefficients based on tracer concentration measurements
A Combinatorial Polynomial Algorithm for the Linear Arrow-Debreu Market
We present the first combinatorial polynomial time algorithm for computing
the equilibrium of the Arrow-Debreu market model with linear utilities.Comment: Preliminary version in ICALP 201
Experimental Analysis of Algorithms for Coflow Scheduling
Modern data centers face new scheduling challenges in optimizing job-level
performance objectives, where a significant challenge is the scheduling of
highly parallel data flows with a common performance goal (e.g., the shuffle
operations in MapReduce applications). Chowdhury and Stoica introduced the
coflow abstraction to capture these parallel communication patterns, and
Chowdhury et al. proposed effective heuristics to schedule coflows efficiently.
In our previous paper, we considered the strongly NP-hard problem of minimizing
the total weighted completion time of coflows with release dates, and developed
the first polynomial-time scheduling algorithms with O(1)-approximation ratios.
In this paper, we carry out a comprehensive experimental analysis on a
Facebook trace and extensive simulated instances to evaluate the practical
performance of several algorithms for coflow scheduling, including the
approximation algorithms developed in our previous paper. Our experiments
suggest that simple algorithms provide effective approximations of the optimal,
and that the performance of our approximation algorithms is relatively robust,
near optimal, and always among the best compared with the other algorithms, in
both the offline and online settings.Comment: 29 pages, 8 figures, 11 table
An Improved Combinatorial Polynomial Algorithm for the Linear Arrow-Debreu Market
We present an improved combinatorial algorithm for the computation of
equilibrium prices in the linear Arrow-Debreu model. For a market with
agents and integral utilities bounded by , the algorithm runs in time. This improves upon the previously best algorithm of Ye by a
factor of \tOmega(n). The algorithm refines the algorithm described by Duan
and Mehlhorn and improves it by a factor of \tOmega(n^3). The improvement
comes from a better understanding of the iterative price adjustment process,
the improved balanced flow computation for nondegenerate instances, and a novel
perturbation technique for achieving nondegeneracy.Comment: to appear in SODA 201
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