Related papers: A Polynomial Time Algorithm for Almost Optimal Ver…
We study efficient algorithms for linear regression and covariance estimation in the absence of Gaussian assumptions on the underlying distributions of samples, making assumptions instead about only finitely-many moments. We focus on how…
Many dynamic graph algorithms have an amortized update time, rather than a stronger worst-case guarantee. But amortized data structures are not suitable for real-time systems, where each individual operation has to be executed quickly. For…
Motivated by multipath routing, we introduce a multi-connected variant of spanners. For that purpose we introduce the $p$-multipath cost between two nodes $u$ and $v$ as the minimum weight of a collection of $p$ internally vertex-disjoint…
In this paper, we obtain a number of new simple pseudo-polynomial time algorithms on the well-known knapsack problem, focusing on the running time dependency on the number of items $n$, the maximum item weight $w_\mathrm{max}$, and the…
In the longest plane spanning tree problem, we are given a finite planar point set $\mathcal{P}$, and our task is to find a plane (i.e., noncrossing) spanning tree for $\mathcal{P}$ with maximum total Euclidean edge length. Despite more…
We prove the following result about approximating the maximum independent set in a graph. Informally, we show that any approximation algorithm with a ``non-trivial'' approximation ratio (as a function of the number of vertices of the input…
We study partial and budgeted versions of the well studied connected dominating set problem. In the partial connected dominating set problem, we are given an undirected graph G = (V,E) and an integer n', and the goal is to find a minimum…
A spanner of a graph is a subgraph that preserves lengths of shortest paths up to a multiplicative distortion. For every $k$, a spanner with size $O(n^{1+1/k})$ and stretch $(2k+1)$ can be constructed by a simple centralized greedy…
Calculating the diameter of an undirected graph requires quadratic running time under the Strong Exponential Time Hypothesis and this barrier works even against any approximation better than 3/2. For planar graphs with positive edge…
Given a graph $G$, and terminal vertices $s$ and $t$, the TRACKING PATHS problem asks to compute a minimum number of vertices to be marked as trackers, such that the sequence of trackers encountered in each s-t path is unique. TRACKING…
The Planar Steiner Tree problem is one of the most fundamental NP-complete problems as it models many network design problems. Recall that an instance of this problem consists of a graph with edge weights, and a subset of vertices (often…
Finding shortest paths in a given network (e.g., a computer network or a road network) is a well-studied task with many applications. We consider this task under the presence of an adversary, who can manipulate the network by perturbing its…
In the area of parameterized complexity, to cope with NP-Hard problems, we introduce a parameter k besides the input size n, and we aim to design algorithms (called FPT algorithms) that run in O(f(k)n^d) time for some function f(k) and…
There are many classical problems in P whose time complexities have not been improved over the past decades. Recent studies of "Hardness in P" have revealed that, for several of such problems, the current fastest algorithm is the best…
Zwick's $(1+\varepsilon)$-approximation algorithm for the All Pairs Shortest Path (APSP) problem runs in time $\widetilde{O}(\frac{n^\omega}{\varepsilon} \log{W})$, where $\omega \le 2.373$ is the exponent of matrix multiplication and $W$…
We give a polynomial time, $(1+\epsilon)$-approximation algorithm for the traveling repairman problem (TRP) in the Euclidean plane and on weighted trees. This improves on the known quasi-polynomial time approximation schemes for these…
Additive spanners are fundamental graph structures with wide applications in network design, graph sparsification, and distance approximation. In particular, a $4$-additive spanner is a subgraph that preserves all pairwise distances up to…
Consider a planar graph $G=(V,E)$ with polynomially bounded edge weight function $w:E\to [0, poly(n)]$. The main results of this paper are NC algorithms for the following problems: - minimum weight perfect matching in $G$, - maximum…
We study optimization problems that are neither approximable in polynomial time (at least with a constant factor) nor fixed parameter tractable, under widely believed complexity assumptions. Specifically, we focus on Maximum Independent…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…