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- Hailiang Liu, Michael Pollack, Haseena Saran
- SIAM J. Scientific Computing
- 2013

In this work, we propose a high-resolution alternating evolution (AE) scheme to solve Hamilton–Jacobi equations. The construction of the AE scheme is based on an alternating evolution system of the Hamilton–Jacobi equation, following the idea previously developed for hyperbolic conservation laws. A semidiscrete scheme derives directly from a sampling of… (More)

- S Johnson, C H Papadimitriou, +13 authors Pr
- 1998

We do not know the integrality ratio for the relaxation we propose. It is possible that a better rounding procedure can be discovered. Here are the worst examples of which we are aware. For k = 3, the following example (which also appeared in 7]) satisses all the new constraints and shows that the integrality ratio is at least 16 15. Consider the graph G =… (More)

- References, K Akeley, +10 authors S V: = W+s
- 2011

An approximate max-ow min-cut theorem for uniform multicommod-ity ow problems with applications to approximation algorithms. Therefore, without loss of generality, we may assume that jS 1 j < p m 1 and proceed recursively to separate V 1 , until a component of the required size is obtained. C(n), the complexity of this procedure, satisses C(n) O(n) +… (More)

- Haseena Saran, Hailiang Liu
- SIAM J. Scientific Computing
- 2011

The alternating evolution (AE) system of Liu [27] ∂tu+ ∂xf(v) = 1 (v − u), ∂tv + ∂xf(u) = 1 (u− v), serves as a refined description of systems of hyperbolic conservation laws ∂tφ+ ∂xf(φ) = 0, φ(x, 0) = φ0(x). The solution of conservation laws is precisely captured when two components take the same initial value as φ0, or approached by two components… (More)

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