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We give polynomial time logarithmic approximation guarantees for the budget minimization, as well as for the profit maximization versions of minimum spanning tree interdiction. In this problem, the goal is to remove some edges of an…
We study the fair k-set selection problem where we aim to select $k$ sets from a given set system such that the (weighted) occurrence times that each element appears in these $k$ selected sets are balanced, i.e., the maximum (weighted)…
In Part II, we study the unweighted Tree Augmentation Problem (TAP) via the Lasserre (Sum~of~Squares) system. We prove that the integrality ratio of an SDP relaxation (the Lasserre tightening of an LP relaxation) is $\leq…
We give a 2-approximation algorithm for Non-Uniform Sparsest Cut that runs in time $n^{O(k)}$, where $k$ is the treewidth of the graph. This improves on the previous $2^{2^k}$-approximation in time $\poly(n) 2^{O(k)}$ due to Chlamt\'a\v{c}…
Energy minimization algorithms, such as graph cuts, enable the computation of the MAP solution under certain probabilistic models such as Markov random fields. However, for many computer vision problems, the MAP solution under the model is…
We consider the task of obtaining the maximum a posteriori estimate of discrete pairwise random fields with arbitrary unary potentials and semimetric pairwise potentials. For this problem, we propose an accurate hierarchical move making…
Recently, Cygan, Kowalik, and Wykurz [IPL 2009] gave sub-exponential-time approximation algorithms for the Set-Cover problem with approximation ratios better than ln(n). In light of this result, it is natural to ask whether such…
While the basic greedy algorithm gives a semi-streaming algorithm with an approximation guarantee of $2$ for the \emph{unweighted} matching problem, it was only recently that Paz and Schwartzman obtained an analogous result for weighted…
For the minimum cardinality vertex cover and maximum cardinality matching problems, the max-product form of belief propagation (BP) is known to perform poorly on general graphs. In this paper, we present an iterative loopy annealing BP…
The Virtual Network Embedding Problem (VNEP) considers the efficient allocation of resources distributed in a substrate network to a set of request networks. Many existing works discuss either heuristics or exact algorithms, resulting in a…
The 'exact subgraph' approach was recently introduced as a hierarchical scheme to get increasingly tight semidefinite programming relaxations of several NP-hard graph optimization problems. Solving these relaxations is a computational…
Matroid interdiction problems are well-researched in the field of combinatorial optimization. In the matroid $\ell$-interdiction problem, an interdiction strategy removes a subset of cardinality $\ell$ from the matroid's ground set. The…
The Gilbert-Pollak Conjecture \citep{gilbert1968steiner}, also known as the Steiner Ratio Conjecture, states that for any finite point set in the Euclidean plane, the Steiner minimum tree has length at least $\sqrt{3}/2 \approx 0.866$ times…
We show that the integrality gap of the natural LP relaxation of the Asymmetric Traveling Salesman Problem is $\text{polyloglog}(n)$. In other words, there is a polynomial time algorithm that approximates the value of the optimum tour…
The maximum common subtree isomorphism problem asks for the largest possible isomorphism between subtrees of two given input trees. This problem is a natural restriction of the maximum common subgraph problem, which is ${\sf NP}$-hard in…
As a variant of the routing and wavelength assignment problem (RWAP), the RWAP with partial path protection (RWAP-PPP) designs a reliable optical-fiber network for telecommunications. It assigns paths and wavelengths to meet communication…
A remarkable connection has been established for antiferromagnetic 2-spin systems, including the Ising and hard-core models, showing that the computational complexity of approximating the partition function for graphs with maximum degree D…
In the classical Steiner tree problem, given an undirected, connected graph $G=(V,E)$ with non-negative edge costs and a set of \emph{terminals} $T\subseteq V$, the objective is to find a minimum-cost tree $E' \subseteq E$ that spans the…
Graph neural networks have been successful in many learning problems and real-world applications. A recent line of research explores the power of graph neural networks to solve combinatorial and graph algorithmic problems such as subgraph…
We present an approximation scheme for minimizing certain Quadratic Integer Programming problems with positive semidefinite objective functions and global linear constraints. This framework includes well known graph problems such as Minimum…