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The Max-Cut problem is a fundamental NP-hard problem, which is attracting attention in the field of quantum computation these days. Regarding the approximation algorithm of the Max-Cut problem, algorithms based on semidefinite programming…
We consider the directed minimum weight cycle problem in the fully dynamic setting. To the best of our knowledge, so far no fully dynamic algorithms have been designed specifically for the minimum weight cycle problem in general digraphs.…
In this paper, we study max-weight stochastic matchings on online bipartite graphs under both vertex and edge arrivals. We focus on designing polynomial time approximation algorithms with respect to the online benchmark, which was first…
The Multiplicative Weights Update (MWU) method is a ubiquitous meta-algorithm that works as follows: A distribution is maintained on a certain set, and at each step the probability assigned to element $\gamma$ is multiplied by $(1 -\epsilon…
In a recent breakthrough, Paz and Schwartzman (SODA'17) presented a single-pass ($2+\epsilon$)-approximation algorithm for the maximum weight matching problem in the semi-streaming model. Their algorithm uses $O(n\log^2 n)$ bits of space,…
We consider a maximum entropy edge weight model for shortest path networks that allows for negative weights. Given a graph $G$ and possible weights $\mathcal{W}$ typically consisting of positive and negative values, the model selects edge…
We study the Maximum Weight Matching (MWM) problem for general graphs through the max-product Belief Propagation (BP) and related Linear Programming (LP). The BP approach provides distributed heuristics for finding the Maximum A Posteriori…
Wattenhofer [WW04] derive a complicated distributed algorithm to compute a weighted matching of an arbitrary weighted graph, that is at most a factor 5 away from the maximum weighted matching of that graph. We show that a variant of the…
Finding a maximum-weight matching is a classical and well-studied problem in computer science, solvable in cubic time in general graphs. We consider the specialization called assignment problem where the input is a bipartite graph, and…
We improve the running times of $O(1)$-approximation algorithms for the set cover problem in geometric settings, specifically, covering points by disks in the plane, or covering points by halfspaces in three dimensions. In the unweighted…
We study the influence of a graph parameter called modular-width on the time complexity for optimally solving well-known polynomial problems such as Maximum Matching, Triangle Counting, and Maximum $s$-$t$ Vertex-Capacitated Flow. The…
We present a combinatorial algorithm for computing exact maximum flows in directed graphs with $n$ vertices and edge capacities from $\{1,\dots,U\}$ in $n^{2+o(1)}\log U$ time, which is almost optimal in dense graphs. Our algorithm is a…
We present approximation algorithms for almost all variants of the multi-criteria traveling salesman problem (TSP). First, we devise randomized approximation algorithms for multi-criteria maximum traveling salesman problems (Max-TSP). For…
The Maximum Weight Independent Set of Polygons problem is a fundamental problem in computational geometry. Given a set of weighted polygons in the 2-dimensional plane, the goal is to find a set of pairwise non-overlapping polygons with…
Combinatorial auctions (CA) are a well-studied area in algorithmic mechanism design. However, contrary to the standard model, empirical studies suggest that a bidder's valuation often does not depend solely on the goods assigned to him. For…
We propose improved exact and heuristic algorithms for solving the maximum weight clique problem, a well-known problem in graph theory with many applications. Our algorithms interleave successful techniques from related work with novel data…
We present parameterized streaming algorithms for the graph matching problem in both the dynamic and the insert-only models. For the dynamic streaming model, we present a one-pass algorithm that, with high probability, computes a…
Non-concave maximization has been the subject of much recent study in the optimization and machine learning communities, specifically in deep learning. Recent papers Ge et al, Lee et al (and references therein) indicate that first order…
We consider the problem of finding \textit{semi-matching} in bipartite graphs which is also extensively studied under various names in the scheduling literature. We give faster algorithms for both weighted and unweighted case. For the…
We develop a new algorithmic technique that allows to transfer some constant time approximation algorithms for general graphs into random order streaming algorithms. We illustrate our technique by proving that in random order streams with…