We consider bicriteria optimization problems and investigate the relationship between two standard approaches to solving them: (i) computing the Pareto curve and (ii) the so-called decision maker’s approach in which both criteria are combined into a single (usually non-linear) objective function. Previous work by Papadimitriou and Yannakakis showed how to efficiently approximate the Pareto curv...

Recent inapproximability results of Sly (2010), together with an approximation algorithm presented by Weitz (2006) establish a beautiful picture for the computational complexity of approximating the partition function of the hard-core model. Let λc(T∆) denote the critical activity for the hard-model on the infinite ∆-regular tree. Weitz presented an FPTAS for the partition function when λ < λc(...

This paper considers a linear relaxation of the cut-based integer programming formulation for the group Steiner tree problem (FGST). We combine the approach of Koufogiannakis and Young (2013) with the nearly-linear time approximation scheme for the minimum cut problem of Christiano et. al (2011) in order to develop a fully polynomial time approximation scheme for FGST problem. Our algorithm ret...

We propose routing algorithms for plug-in hybrid electric vehicles (PHEVs) that account for the significant energy efficiency differences of vehicle operating modes and recommend the predominant mode of operation for each road segment during route planning. This is to enhance fuel economy and reduce emissions. We introduce the Energy-Efficient Routing problem (EERP) for PHEVs, and formulate thi...

We study convergence of ε-Nash dynamics in congestion games when delay functions of all resources are similar. Delay functions are said to be similar if their values are within a polynomial factor at every congestion level. We show that for any ε > 0, an ε-Nash dynamics in symmetric congestion games with similar resources converge in steps polynomial in 1/ε and the number of players are resourc...

Given a single machine and a set of jobs with due dates, the classical NP-hard problem of scheduling to minimize total tardiness is a well-understood one. Lawler gave an FPTAS for it some twenty years ago. If the jobs have positive weights the problem of minimizing total weighted tardiness seems to be considerably more intricate. In this paper, we give some of the first approximation algorithms...

We consider the classical scheduling problem on parallel identical machines to minimize the makespan. Under the exponential time hypothesis (ETH), lower bounds on the running times of exact and approximation algorithms are characterized. We achieve the following results: (1) For scheduling on a constant number m of identical machines, denoted by Pm||Cmax, a fully polynomial time approximation s...

Consider the following problem. A seller has infinite copies of n products represented by nodes in a graph. There are m consumers, each has a budget and wants to buy two products. Consumers are represented by weighted edges. Given the prices of products, each consumer will buy both products she wants, at the given price, if she can afford to. Our objective is to help the seller price the produc...

We study the task of gathering k energy-constrained mobile agents in an undirected edge-weighted graph. Each agent is initially placed on arbitrary node and has a limited amount energy, which constrains distance it can move. Since this may render at single point impossible, we three variants near-gathering: The goal to move into configuration that minimizes either (i) radius ball containing all...