Related papers: Polynomial-time approximation scheme for Max-Cut p…

The max-cut problem is a classical graph theory problem which is NP-complete. The best polynomial time approximation scheme relies on \emph{semidefinite programming} (SDP). We study the conditions under which graphs of certain classes have…

We give a direct polynomial-time reduction from parity games played over the configuration graphs of collapsible pushdown systems to safety games played over the same class of graphs. That a polynomial-time reduction would exist was known…

We study the MaxCut problem for graphs $G=(V,E)$. The problem is NP-hard, there are two main approximation algorithms with theoretical guarantees: (1) the Goemans \& Williamson algorithm uses semi-definite programming to provide a…

We study the computational complexity of approximating general constrained Markov decision processes. Our primary contribution is the design of a polynomial time $(0,\epsilon)$-additive bicriteria approximation algorithm for finding optimal…

In the maximum constraint satisfaction problem (Max CSP), one is given a finite collection of (possibly weighted) constraints on overlapping sets of variables, and the goal is to assign values from a given domain to the variables so as to…

The $k$-cut problem asks, given a connected graph $G$ and a positive integer $k$, to find a minimum-weight set of edges whose removal splits $G$ into $k$ connected components. We give the first polynomial-time algorithm with approximation…

The Restricted Assignment Problem is a prominent special case of Scheduling on Parallel Unrelated Machines. For the strongest known linear programming relaxation, the configuration LP, we improve the non-constructive bound on its…

We revisit the classic #Knapsack problem, which asks to count the Boolean points $(x_1,\dots,x_n)\in\{0,1\}^n$ in a given half-space $\sum_{i=1}^nW_ix_i\le T$. This #P-complete problem admits $(1\pm\epsilon)$-approximation. Before this…

Assuming the Unique Games Conjecture (UGC), the best approximation ratio that can be obtained in polynomial time for the MAX CUT problem is $\alpha_{\text{CUT}}\simeq 0.87856$, obtained by the celebrated SDP-based approximation algorithm of…

We design new approximation algorithms for the Multiway Cut problem, improving the previously known factor of 1.32388 [Buchbinder et al., 2013]. We proceed in three steps. First, we analyze the rounding scheme of Buchbinder et al., 2013 and…

MAX CLIQUE problem (MCP) is an NPO problem, which asks to find the largest complete sub-graph in a graph $G, G = (V, E)$ (directed or undirected). MCP is well known to be $NP-Hard$ to approximate in polynomial time with an approximation…

Max-k-Cut and correlation clustering are fundamental graph partitioning problems. For a graph with G=(V,E) with n vertices, the methods with the best approximation guarantees for Max-k-Cut and the Max-Agree variant of correlation clustering…

In this paper we study the MAX-CUT problem on power law graphs (PLGs) with power law exponent $\beta$. We prove some new approximability results on that problem. In particular we show that there exist polynomial time approximation schemes…

We give a deterministic, polynomial-time algorithm for approximately counting the number of {0,1}-solutions to any instance of the knapsack problem. On an instance of length n with total weight W and accuracy parameter eps, our algorithm…

We initiate the systematic study of a recently introduced polynomial-time analogue of MaxSNP, which includes a large number of well-studied problems (including Nearest and Furthest Neighbor in the Hamming metric, Maximum Inner Product,…

The Clique Problem has a reduction to the Maximum Flow Network Interdiction Problem. We review the reduction to evolve a polynomial time algorithm for the Clique Problem. A computer program in C language has been written to validate the…

We study polynomial-time approximation algorithms for the Quantum Max-Cut (QMC) problem. Given an edge-weighted graph $G$ on n vertices, the QMC problem is to determine the largest eigenvalue of a particular $2^n \times 2^n$ matrix that…

We initiate the algorithmic study of the Quantum Max-$d$-Cut problem, a quantum generalization of the well-known Max-$d$-Cut problem. The Quantum Max-$d$-Cut problem involves finding a quantum state that maximizes the expected energy…

I present a single algorithm which solves the clique problems, "What is the largest size clique?", "What are all the maximal cliques?" and the decision problem, "Does a clique of size k exist?" for any given graph in polynomial time. The…

Given an edge-weighted graph $G$ on $n$ nodes, the NP-hard Max-Cut problem asks for a node bipartition such that the sum of edge weights joining the different partitions is maximized. We propose a fixed-parameter tractable algorithm…