Related papers: Solve For Shortest Paths Problem Within Logarithm …
The problem of finding multiple simple shortest paths in a weighted directed graph $G=(V,E)$ has many applications, and is considerably more difficult than the corresponding problem when cycles are allowed in the paths. Even for a single…
We study the use of machine learning techniques to solve a fundamental shortest path problem, known as the single-source many-targets shortest path problem (SSMTSP). Given a directed graph with non-negative edge weights, our goal is to…
Finding diverse solutions in combinatorial problems recently has received considerable attention (Baste et al. 2020; Fomin et al. 2020; Hanaka et al. 2021). In this paper we study the following type of problems: given an integer $k$, the…
Several goal-oriented problems in the real-world can be naturally expressed as Stochastic Shortest Path Problems (SSPs). However, the computational complexity of solving SSPs makes finding solutions to even moderately sized problems…
With the pervasiveness of Stochastic Shortest-Path (SSP) problems in high-risk industries, such as last-mile autonomous delivery and supply chain management, robust planning algorithms are crucial for ensuring successful task completion…
The GC problem is to identify a pre-determined number of center vertices such that the distances or costs from (or to) the centers to (or from) other vertices is minimized. The bottleneck of a path is the minimum capacity of edges on the…
Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct randomized algorithm for solving large, weakly constrained SDP…
The constrained path optimization (CPO) problem takes the following input: (a) a road network represented as a directed graph, where each edge is associated with a "cost" and a "score" value; (b) a source-destination pair and; (c) a budget…
Despite major advancements in nonlinear programming (NLP) and convex relaxations, most system operators around the world still predominantly use some form of linear programming (LP) approximation of the AC power flow equations. This is…
Cycle packing is a fundamental problem in optimization, graph theory, and algorithms. Motivated by recent advancements in finding vertex-disjoint paths between a specified set of vertices that either minimize the total length of the paths…
Stochastic shortest path (SSP) problems arise in a variety of discrete stochastic control contexts. An optimal solutions to such a problem is typically computed using the value function, which can be found by solving the corresponding…
The classic problem of constrained pathfinding is a well-studied, yet challenging, topic in AI with a broad range of applications in various areas such as communication and transportation. The Weight Constrained Shortest Path Problem…
Given an undirected $n$-vertex graph and $k$ pairs of terminal vertices $(s_1,t_1), \ldots, (s_k,t_k)$, the $k$-Disjoint Shortest Paths ($k$-DSP)-problem asks whether there are $k$ pairwise vertex-disjoint paths $P_1,\ldots, P_k$ such that…
Semidefinite programs (SDP) are one of the most versatile frameworks in numerical optimization, serving as generalizations of many conic programs and as relaxations of NP-hard combinatorial problems. Their main drawback is their…
The CLP scheme uses Horn clauses and SLD resolution to generate multiple constraint satisfaction problems (CSPs). The possible CSPs include rational trees (giving Prolog) and numerical algorithms for solving linear equations and linear…
Network virtualization has become a fundamental technology to deliver services for emerging data-intensive applications in fields such as bioinformatics and retail analytics hosted at multi-data center scales. To create and maintain a…
We propose a new exact approach for solving integer linear programming (ILP) problems which we will call projective splitting algorithms (PSAs). Unlike classical methods for solving ILP problems, PSAs conduct the search for the optimal…
Given a graph, the shortest-path problem requires finding a sequence of edges with minimum cumulative length that connects a source vertex to a target vertex. We consider a variant of this classical problem in which the position of each…
Given a graph $G$, and terminal vertices $s$ and $t$, the TRACKING PATHS problem asks to compute a minimum number of vertices to be marked as trackers, such that the sequence of trackers encountered in each s-t path is unique. TRACKING…
Algorithms for computing All-Pairs Shortest-Paths (APSP) are critical building blocks underlying many practical applications. The standard sequential algorithms, such as Floyd-Warshall and Johnson, quickly become infeasible for large input…