CMSC858F: Algorithmic Lower Bounds: Fun with Hardness Proofs Project A Two Stage Allocation Problem
نویسندگان
چکیده
Consider a good (such as a hotel room) which, if not sold on time, is worth nothing to the seller. For a customer who is considering a choice of such goods, their prices may change dramatically by the time the customer needs to use the good; thus a customer who is aware of this fact might choose to gamble, delaying buying until the last moment in the hopes of better prices. While this gamble can yield large savings, it also carries much risk. However, a coordinator can offer customers a compromise between these extremes and benefits in aggregate. Here we explore how a coordinator might profit from forecasts of such future price fluctuations. Our results can be used in a general setting where customers buy products or services in advance and where market prices may significantly change in the future.
منابع مشابه
CMSC858F: Algorithmic Lower Bounds: Fun with Hardness Proofs
1. For any instance I1 of π1, I2 = f(I1) is an instance of π2 such that OPTπ2(I2) ≤ OPTπ1(I1). 2. For any feasible solution S2 of I2, S1 = g(I1, S2) (g maps S2 into an instance of I1) we have Costπ1(I1, S1) ≤ Costπ2(I2, S2). Note that OPTπ2(I2) ≤ OPTπ1(I1) ≤ Costπ1(I1, S1) ≤ Costπ2(I2, S2). Therefore, if there is an approximation factor ∆ for π2 then there is an approximation factor ∆ for π1 as...
متن کاملCMSC 858F: Algorithmic Lower Bounds: Fun with Hardness Proofs Fall 2014 Cubic hardness and all-pair shortest paths
In the next two lectures, we look at lower bounds conjectured on two important and well-known problems. One is the All-Pairs-Shortest-Path(APSP) problem which is believed to be truly cubic(i.e. there is no exact algorithm for this problem which runs in time O(n ) for a constant > 0). The second problem considered is the 3−SUM problem which is conjectured to be truly quadratic(i.e. there is no e...
متن کاملAlgorithmic Lower Bounds : Fun With Hardness Proofs Fall 2014 Lecture 3 Scribe Notes
Last time, we established the hardness of two fundamental problems, (2-)Partition and 3-Partition, and exhibited a bunch of reductions from those problems to other numerical and geometrical ones. Today, we continue with reductions from 3and 2-Partition to geometrical problems—we’ll also use the fact that the problem of packing n squares into a square without rotations is strongly NP-complete, a...
متن کاملCMSC 858F: Algorithmic Lower Bounds: Fun with Hardness Proofs Fall 2014 Quadratic Hardness and the 3-SUM Problem
In the previous lecture, we looked at the APSP problem and some of the other closely related problems. We studied the cubic hardness of these problems. In this lecture, we will go about doing something similar, but in the domain of quadratic hardness. With regard to this, we will choose 3-SUM problem as the representative problem. We will look at some related problems, that can be reduced to th...
متن کاملCMSC 858F: Algorithmic Lower Bounds: Fun with Hardness Proofs Fall 2014 Fixed Parameter Algorithms and Lower Bounds for parameterized Problems
Unless P = NP we have to satisfy ourselves with any two out of the three goals. Most of the early undergrad algorithms like matching, shortest path etc. are exact and fast. To tackle hard problems and obtain a fast solution we use approximation algorithms, PTAS etc. FPT or fixed parameter tractable algorithms come to our rescue when we need to tackle hard problems yet obtain an optimal solution...
متن کامل