Related papers: A Linear Programming Based Approach to the Steiner…
In this paper, we study the relations between the numerical structure of the optimal solutions of a convex programming problem defined on the edge set of a simple graph and the stability number (i.e. the maximum size of a subset of pairwise…
Graph theory has been a powerful tool in solving difficult and complex problems arising in all disciplines. In particular, graph matching is a classical problem in pattern analysis with enormous applications. Many graph problems have been…
Given a simple connected undirected graph G = (V, E), a set X \subseteq V(G), and integers k and p, STEINER SUBGRAPH EXTENSION problem asks if there exists a set S \supseteq X with at most k vertices such that G[S] is p-edge-connected. This…
The $k$-Steiner-2NCS problem is as follows: Given a constant $k$, and an undirected connected graph $G = (V,E)$, non-negative costs $c$ on $E$, and a partition $(T, V-T)$ of $V$ into a set of terminals, $T$, and a set of non-terminals (or,…
The pooling problem is an important industrial problem in the class of network flow problems for allocating gas flow in pipeline transportation networks. For P-formulation of the pooling problem with time discretization, we propose second…
It is well known that the most challenging question in optimization and discrete geometry is whether there is a strongly polynomial time simplex algorithm for linear programs (LPs). This paper gives a positive answer to this question by…
This dissertation investigates integer linear programming (ILP) formulation of Bayesian Network structure learning problem. We review the definition and key properties of Bayesian network and explain score metrics used to measure how well…
Uniform cost-distance Steiner trees minimize the sum of the total length and weighted path lengths from a dedicated root to the other terminals. They are applied when the tree is intended for signal transmission, e.g. in chip design or…
An integer program (IP) with a finite number of feasible solutions may have an unbounded linear programming relaxation if it contains irrational parameters, due to implicit constraints enforced by the irrational numbers. We show that those…
Lagrangian Relaxation (LR) is a powerful technique for solving large-scale Mixed Integer Linear Programming (MILP), particularly those with decomposable structures, such as vehicle routing or unit commitment problems. By relaxing the…
We design the first online algorithm with poly-logarithmic competitive ratio for the edge-weighted degree-bounded Steiner forest(EW-DB-SF) problem and its generalized variant. We obtain our result by demonstrating a new generic approach for…
In the Directed Steiner Tree (DST) problem the input is a directed edge-weighted graph $G=(V,E)$, a root vertex $r$ and a set $S \subseteq V$ of $k$ terminals. The goal is to find a min-cost subgraph that connects $r$ to each of the…
We give an overview of new and existing cut- and flow-based ILP formulations for the two-stage stochastic Steiner tree problem and compare the strength of the LP relaxations.
We study the problem of scheduling a general computational DAG on multiple processors in a 2-level memory hierarchy. This setting is a natural generalization of several prominent models in the literature, and it simultaneously captures…
In the Steiner Tree problem we are given an edge weighted undirected graph $G = (V,E)$ and a set of terminals $R \subseteq V$. The task is to find a connected subgraph of $G$ containing $R$ and minimizing the sum of weights of its edges. We…
The Steiner Forest problem is an important generalization of the Steiner Tree problem. We are given an undirected graph with nonnegative edge costs and a collection of pairs of vertices. The task is to compute a cheapest forest with the…
We propose a trust-region method that solves a sequence of linear integer programs to tackle integer optimal control problems regularized with a total variation penalty. The total variation penalty allows us to prove the existence of…
Given an edge-weighted graph and a set of known seed vertices, a network scientist often desires to understand the graph relationships to explain connections between the seed vertices. When the seed set is 3 or larger Steiner minimal tree -…
A sequential piecewise linear programming method is presented where bounded domains of non-convex functions are successively contracted about the solution of a piecewise linear program at each iteration of the algorithm. Although…
This paper deals with the computation of polytopic invariant sets for polynomial dynamical systems. An invariant set of a dynamical system is a subset of the state space such that if the state of the system belongs to the set at a given…