Related papers: A Bad Example for Jain's Iterative Rounding Theore…
Iterative rounding has enjoyed tremendous success in elegantly resolving open questions regarding the approximability of problems dominated by covering constraints. Although iterative rounding methods have been applied to packing problems,…
Iterative rounding and relaxation have arguably become the method of choice in dealing with unconstrained and constrained network design problems. In this paper we extend the scope of the iterative relaxation method in two directions: (1)…
In the Cover Small Cuts problem, we are given a capacitated (undirected) graph $G=(V,E,u)$ and a threshold value $\lambda$, as well as a set of links $L$ with end-nodes in $V$ and a non-negative cost for each link $\ell\in L$; the goal is…
We consider the problem of finding a minimum edge cost subgraph of a graph satisfying both given node-connectivity requirements and degree upper bounds on nodes. We present an iterative rounding algorithm of the biset LP relaxation for this…
In this paper, we consider the network slicing problem which attempts to map multiple customized virtual network requests (also called services) to a common shared network infrastructure and allocate network resources to meet diverse…
Combinatorial problems are formulated to find optimal designs within a fixed set of constraints. They are commonly found across diverse engineering and scientific domains. Understanding how to best use quantum computers for combinatorial…
The vertex cover problem is a fundamental and widely studied combinatorial optimization problem. It is known that its standard linear programming relaxation is integral for bipartite graphs and half-integral for general graphs. As a…
The classic lower bound of Kuhn, Moscibroda and Wattenhofer [JACM 2016] states that approximate maximum matching and approximate vertex cover (among other problems) in the LOCAL model require $\Omega(\min\{\sqrt{\frac{\log n}{\log\log n}},…
In a standard $f$-connectivity network design problem, we are given an undirected graph $G=(V,E)$, a cut-requirement function $f:2^V \rightarrow {\mathbb{N}}$, and non-negative costs $c(e)$ for all $e \in E$. We are then asked to find a…
We introduce a new iterative rounding technique to round a point in a matroid polytope subject to further matroid constraints. This technique returns an independent set in one matroid with limited violations of the other ones. On top of the…
In this paper, we initiate a theoretical study of what we call the join covering problem. We are given a natural join query instance $Q$ on $n$ attributes and $m$ relations $(R_i)_{i \in [m]}$. Let $J_{Q} = \ \Join_{i=1}^m R_i$ denote the…
Typical behavior of the linear programming (LP) problem is studied as a relaxation of the minimum vertex cover, a type of integer programming (IP) problem. A lattice-gas model on the Erd\"os-R\'enyi random graphs of $\alpha$-uniform…
In many iterative optimization methods, fixed-point theory enables the analysis of the convergence rate via the contraction factor associated with the linear approximation of the fixed-point operator. While this factor characterizes the…
We show that under mild assumptions for a problem whose solutions admit a dynamic programming-like recurrence relation, we can still find a solution under additional packing constraints, which need to be satisfied approximately. The number…
We revisit the minimum dominating set problem on graphs with arboricity bounded by $\alpha$. Bansal and Umboh [BU17] gave an $O(\alpha)$-approximation LP rounding algorithm, which also translates into a near-linear time algorithm using…
The quadratic cycle cover problem is the problem of finding a set of node-disjoint cycles visiting all the nodes such that the total sum of interaction costs between consecutive arcs is minimized. In this paper we study the linearization…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…
We study problems related to connecting multi-interface networks of wireless devices. These problems are modeled using graphs, where vertices represent the devices and edges represent potential communication links. Each vertex can activate…
We study how much a linear program (LP) can be compressed when solved repeatedly, given prior knowledge about its objective function. Existing data-driven projection methods learn low-dimensional surrogate LPs with approximate…
In this paper we show how to combine two algorithmic techniques to obtain linear time algorithms for various optimization problems on graphs, and present a subroutine which will be useful in doing so. The first technique is iterative…