Related papers: On the optimal relaxation parameter of graph-based…
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…
A useful approach to the mathematical analysis of large-scale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems associated to finding decompositions…
This paper provides a theoretical and numerical comparison of classical first-order splitting methods for solving smooth convex optimization problems and cocoercive equations. From a theoretical point of view, we compare convergence rates…
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 propose a convex-concave programming approach for the labeled weighted graph matching problem. The convex-concave programming formulation is obtained by rewriting the weighted graph matching problem as a least-square problem on the set…
In this paper, we develop a novel weighted Laplacian method, which is partially inspired by the theory of graph Laplacian, to study recent popular graph problems, such as multilevel graph partitioning and balanced minimum cut problem, in a…
The recently introduced $\{k\}$-packing function problem is considered in this paper. Special relation between a case when $k=1$, $k\ge 2$ and linear programming relaxation is introduced with sufficient conditions for optimality. For…
Numerous approximation algorithms for problems on unit disk graphs have been proposed in the literature, exhibiting a sharp trade-off between running times and approximation ratios. We introduce a variation of the known shifting strategy…
In this paper, we consider classic randomized low diameter decomposition procedures for planar graphs that obtain connected clusters which are cohesive in that close-by pairs of nodes are assigned to the same cluster with high probability.…
For distributed graph processing on massive graphs, a graph is partitioned into multiple equally-sized parts which are distributed among machines in a compute cluster. In the last decade, many partitioning algorithms have been developed…
In this paper, we propose a general graph optimization based framework for localization, which can accommodate different types of measurements with varying measurement time intervals. Special emphasis will be on range-based localization.…
Douglas-Rachford splitting and the alternating direction method of multipliers (ADMM) can be used to solve convex optimization problems that consist of a sum of two functions. Convergence rate estimates for these algorithms have received…
We consider the problems of finding optimal identifying codes, (open) locating-dominating sets and resolving sets of an interval or a permutation graph. In these problems, one asks to find a subset of vertices, normally called a…
The graph isomorphism problem looks deceptively simple, but although polynomial-time algorithms exist for certain types of graphs such as planar graphs and graphs with bounded degree or eigenvalue multiplicity, its complexity class is still…
Finding a maximum cut is a fundamental task in many computational settings. Surprisingly, it has been insufficiently studied in the classic distributed settings, where vertices communicate by synchronously sending messages to their…
We present a new algorithmic paradigm for the decentralized solution of graph-structured optimization problems that arise in the estimation and control of network systems. A key and novel design concept of the proposed approach is that it…
A dynamic graph algorithm is a data structure that answers queries about a property of the current graph while supporting graph modifications such as edge insertions and deletions. Prior work has shown strong conditional lower bounds for…
Real-world graphs, such as social networks, financial transactions, and recommendation systems, often demonstrate dynamic behavior. This phenomenon, known as graph stream, involves the dynamic changes of nodes and the emergence and…
Graph partitioning is a key fundamental problem in the area of big graph computation. Previous works do not consider the practical requirements when optimizing the big data analysis in real applications. In this paper, motivated by…
We study sublinear algorithms for two fundamental graph problems, MAXCUT and correlation clustering. Our focus is on constructing core-sets as well as developing streaming algorithms for these problems. Constant space algorithms are known…