We introduce the notion of a stable instance for a discrete optimization problem, and argue that in many practical situations only sufficiently stable instances are of interest. The question then arises whether stable instances of NP–hard problems are easier to solve. In particular, whether there exist algorithms that solve correctly and in polynomial time all sufficiently stable instances of s...

Given an undirected graph G = (V,E) with a terminal set S ⊆ V , a weight function μ : ( S 2 ) → Z+ on terminal pairs, and an edge-cost a : E → Z+, the μweighted minimum-cost edge-disjoint S-paths problem (μ-CEDP) is to maximize ∑ P∈P μ(sP , tP )−a(P ) over all edge-disjoint sets P of S-paths, where sP , tP denote the ends of P and a(P ) is the sum of edge-cost a(e) over edges e in P . Our main ...

We study the max-min fair allocation problem in which a set of m indivisible items are to be distributed among n agents such that the minimum utility among all agents is maximized. In the restricted setting, the utility of each item j on agent i is either 0 or some non-negative weight wj . For this setting, Asadpour et al. [2] showed that a certain configuration-LP can be used to estimate the o...

We study a problem of multi-resource fair allocation with bounded number of tasks, and propose the lexicographically max-min dominant share (LMMDS) fair allocation mechanism, which is a generalization of the popular dominant resource fairness (DRF) mechanism. We prove that LMMDS satisfies sharing incentives, group strategyproofness, envy-freeness, and Pareto efficiency, by exploiting the proper...

In this paper we study similarity measures for moving curves which can, for example, model changing coastlines or retreating glacier termini. Points on a moving curve have two parameters, namely the position along the curve as well as time. We therefore focus on similarity measures for surfaces, specifically the Fréchet distance between surfaces. While the Fréchet distance between surfaces is n...

In this paper we describe a problem that we de ne as the Budget-Constrained Minimum Cost Flow (BCMCF) problem. The BCMCF problem is a natural extension of the well-known Minimum Cost Flow (MCF) [2] problem, with a xed cost related to the use of arcs and a budget constraint. Network ow problems often become hard when extra constraints are added. Ahuja and Orlin [1] discuss the constrained maximu...

Fast algorithm for joint near-optimal approximation of multiple polygonal curves is proposed. It is based on iterative reduced-search dynamic programming introduced earlier for the minproblem of a single polygonal curve. The proposed algorithm jointly optimizes the number of line segments allocated to the different individual curves, and the approximation of the curves by the given number of se...