Analysis for Applied Mathematics

Cheney, Ward

doi:10.1007/978-1-4757-3559-8

Cited by 89 publications

(77 citation statements)

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“…Then, we remove one of the edges which has the most intersections with the other convex hull (lines [5][6][7][8]. We start to add free we call a red (blue) point free if it is not connected to the red (blue) chain yet.…”

Section: The Proposed Algorithmmentioning

confidence: 99%

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Time complexity of two disjoint simple paths

Razzazi

Sepahvand

2017

Scientia Iranica

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Abstract. Finding two disjoint simple paths on two given sets of points is a geometric problem introduced by Je Erickson. This problem has various applications in computational geometry, e.g. robot motion planning, generating polygon, etc. We will present a reduction from planar Hamiltonian path to this problem, and prove that it is NPcomplete. To the best of our knowledge, no study has considered its complexity up until now. We also present a reduction from planar Hamiltonian path problem to the problem of \ nding a path on given points in the presence of arbitrary obstacles" and prove that it is also NP-complete. Also, we present a heuristic algorithm with time complexity of O(n 4 ) to solve this problem. The proposed algorithm rst calculates the convex hull for each of the entry points and then produces two simple paths on the two entry point sets.

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Section: The Proposed Algorithmmentioning

confidence: 99%

“…The points are in general position. A simple path may also be called polygonal chain, polygonal curve [5], polygonal path [6], polyline [7], or piecewise linear curve [7]. This problem has many potential applications in computational geometry, e.g.…”

Section: Introductionmentioning

confidence: 99%

Time complexity of two disjoint simple paths

Razzazi

Sepahvand

2017

Scientia Iranica

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“…Similarly to Section 3.2, we analyze the buyer's problem at his arriving time in order to compute R(H), the best-response participation strategy given that all other buyers use the strategy H. As we 9 Note that in this case QT is not a fixed quantity but a random variable that depends on the initial number of units Q0 and the number of buyers that select the fixed price channel during [0, T ). The strategy is dominant even for this case where the number of units to auction QT is uncertain.…”

Section: Characterization Of a Symmetric Participation Equilibrium H(v)mentioning

confidence: 99%

“…From this last inequality, it follows that the right-hand side h H (v τ ) is the natural candidate for best-response strategy for buyer τ with valuation v τ >P . However, for an arbitrary H ∈ H, h H (v τ ) is not guaranteed to be nonnegative and so h H is not necessarily a well-defined participation strategy in H. Fortunately, note that we can correct this problem by simply setting the best-response strategy R(H)(v τ ) = (h H (v τ )) + which is equivalent to (12) and consistent with (9).…”

Section: Proof Of Propositionmentioning

confidence: 99%

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Online Auction and List Price Revenue Management

2007

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We analyze a revenue management problem in which a seller facing a Poisson arriving stream of customers operates an online multiunit auction. Customers have an alternative list price channel where to get the product from. We consider two variants of this problem: In the first one, the list price is an external channel run by another firm. In the second variant, the seller manages simultaneously both the auction and the list price channels.Each consumer, trying to maximize his own surplus, must decide either to buy at the posted price and get the item at no risk, or to join the auction and wait until its end, where the winners are revealed and the auction price is disclosed.Our approach consists of two parts. First, we study structural properties of the problem, and show that the equilibrium strategy for both versions of this game is of the threshold type, meaning that a consumer will join the auction only if his arrival time is above a function of his own valuation. This consumer's strategy can be computed using an iterative algorithm in a function space, provably convergent under some conditions. Unfortunately, this procedure is computationally intensive.To overcome this, we formulate an asymptotic version of the problem, in which the demand rate and the initial number of units grow proportionally large. We get a simple closed form for the equilibrium strategy in this regime, which is then used as an approximated solution for the original problem. Numerical computations show that this heuristic is very accurate. The asymptotic solution culminates then in simple and precise recipes for how bidders should behave, and how the seller should structure the auction, and price the product in the dual channel case.

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Linear vs. nonlinear selection for the propagation speed of the solutions of scalar reaction‐diffusion equations invading an unstable equilibrium

Lucia

Muratov

Novaga

2004

Comm Pure Appl Math

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We revisit the classical problem of speed selection for the propagation of disturbances in scalar reaction-diffusion equations with one linearly stable and one linearly unstable equilibrium. For a wide class of initial data this problem reduces to finding the minimal speed of the monotone traveling wave solutions connecting these two equilibria in one space dimension. We introduce a variational characterization of these traveling wave solutions and give a necessary and sufficient condition for linear versus nonlinear selection mechanism. We obtain sufficient conditions for the linear and nonlinear selection mechanisms that are easily verifiable. Our method, also allows us to obtain efficient lower and upper bounds for the propagation speed

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Analysis for Applied Mathematics

Cited by 89 publications

References 0 publications

Time complexity of two disjoint simple paths

Time complexity of two disjoint simple paths

Online Auction and List Price Revenue Management

Linear vs. nonlinear selection for the propagation speed of the solutions of scalar reaction‐diffusion equations invading an unstable equilibrium

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