Register Loading via Linear Programming

We study the following optimization problem. The input is a number k and a directed graph with a specified “start ” vertex, each of whose vertices may have one “memory bank requirement”, an integer. There are k “registers”, labeled 1...k. A valid solution associates to the vertices with no bank requirement one or more “load instructions ” L[b,j], for bank b and register j, such that every directed trail from the start vertex to some vertex with bank requirement c contains a vertex u that has been associated L[c,i] (for some register i ≤ k) and no vertex following u in the trail has been associated an L[b,i], for any other bank b. The objective is to minimize the total number of associated load instructions. We give a k(k +1)-approximation algorithm based on linear programming rounding, with (k+1) being the best possible unless Vertex Cover has approximation 2−ǫ for ǫ> 0. We also present a O(klogn) approximation, with n being the number of vertices in the input directed graph. Based on the same linear program, another rounding method outputs a valid solution with objective at most 2k times the optimum for k registers, using 2k−1 registers. This version of the paper corrects some minor errors that made it in the final Algorithmica paper.

Facility location with double-peaked preference

We study the problem of locating a single facility on a real line based on the reports of self-interested agents, when agents have double-peaked preferences, with the peaks being on opposite sides of their locations. We observe that double-peaked preferences capture real-life scenarios and thus complement the well-studied notion of single-peaked preferences. We mainly focus on the case where peaks are equidistant from the agents' locations and discuss how our results extend to more general settings. We show that most of the results for single-peaked preferences do not directly apply to this setting; this makes the problem essentially more challenging. As our main contribution, we present a simple truthful-in-expectation mechanism that achieves an approximation ratio of 1+b/c for both the social and the maximum cost, where b is the distance of the agent from the peak and c is the minimum cost of an agent. For the latter case, we provide a 3/2 lower bound on the approximation ratio of any truthful-in-expectation mechanism. We also study deterministic mechanisms under some natural conditions, proving lower bounds and approximation guarantees. We prove that among a large class of reasonable mechanisms, there is no deterministic mechanism that outperforms our truthful-in-expectation mechanism

Min-energy scheduling for aligned jobs in accelerate model

AbstractA dynamic voltage scaling technique provides the capability for processors to adjust the speed and control the energy consumption. We study the pessimistic accelerate model where the acceleration rate of the processor speed is at most K and jobs cannot be executed during the speed transition period. The objective is to find a min-energy (optimal) schedule that finishes every job within its deadline. The job set we study in this paper is aligned jobs where earlier released jobs have earlier deadlines. We start by investigating a special case where all jobs have a common arrival time and design an O(n2) algorithm to compute the optimal schedule based on some nice properties of the optimal schedule. Then, we study the general aligned jobs and obtain an O(n2) algorithm to compute the optimal schedule by using the algorithm for the common arrival time case as a building block. Because our algorithm relies on the computation of the optimal schedule in the ideal model (K=∞), in order to achieve O(n2) complexity, we improve the complexity of computing the optimal schedule in the ideal model for aligned jobs from the currently best known O(n2logn) to O(n2)

Facility Location Games with Ordinal Preferences

We consider a new setting of facility location games with ordinal preferences. In such a setting, we have a set of agents and a set of facilities. Each agent is located on a line and has an ordinal preference over the facilities. Our goal is to design strategyproof mechanisms that elicit truthful information (preferences and/or locations) from the agents and locate the facilities to minimize both maximum and total cost objectives as well as to maximize both minimum and total utility objectives. For the four possible objectives, we consider the 2-facility settings in which only preferences are private, or locations are private. For each possible combination of the objectives and settings, we provide lower and upper bounds on the approximation ratios of strategyproof mechanisms, which are asymptotically tight up to a constant. Finally, we discuss the generalization of our results beyond two facilities and when the agents can misreport both locations and preferences

Strategyproof Mechanisms For Group-Fair Facility Location Problems

We study the facility location problems where agents are located on a real line and divided into groups based on criteria such as ethnicity or age. Our aim is to design mechanisms to locate a facility to approximately minimize the costs of groups of agents to the facility fairly while eliciting the agents' locations truthfully. We first explore various well-motivated group fairness cost objectives for the problems and show that many natural objectives have an unbounded approximation ratio. We then consider minimizing the maximum total group cost and minimizing the average group cost objectives. For these objectives, we show that existing classical mechanisms (e.g., median) and new group-based mechanisms provide bounded approximation ratios, where the group-based mechanisms can achieve better ratios. We also provide lower bounds for both objectives. To measure fairness between groups and within each group, we study a new notion of intergroup and intragroup fairness (IIF) . We consider two IIF objectives and provide mechanisms with tight approximation ratios

An FPTAS of Minimizing Total Weighted Completion Time on Single Machine with Position Constraint

In this paper we study the classical scheduling problem of minimizing the total weighted completion time on a single machine with the constraint that one specific job must be scheduled at a specified position. We give dynamic programs with pseudo-polynomial running time, and a fully polynomial-time approximation scheme (FPTAS)