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Path cover is a well-known intractable problem that finds a minimum number of vertex disjoint paths in a given graph to cover all the vertices. We show that a variant, where the objective function is not the number of paths but the number…
Today mobile users such as drivers are invited by content providers (e.g., Tripadvisor) to sample fresh information of diverse paths to control the age of information (AoI). However, selfish drivers prefer to travel through the shortest…
We study the allocation of indivisible goods that form an undirected graph and quantify the loss of fairness when we impose a constraint that each agent must receive a connected subgraph. Our focus is on well-studied fairness notions…
We consider a network pricing game on a parallel network with congestion effects in which link owners set tolls for travel so as to maximize profit. A central authority is able to regulate this competition by means of a (uniform) price cap.…
We study the NP-hard problem of approximating a Minimum Routing Cost Spanning Tree in the message passing model with limited bandwidth (CONGEST model). In this problem one tries to find a spanning tree of a graph $G$ over $n$ nodes that…
The shortest path problem in graphs is a cornerstone of AI theory and applications. Existing algorithms generally ignore edge weight computation time. We present a generalized framework for weighted directed graphs, where edge weight can be…
Given a graph $G=(V, E)$, the problem of Graph Burning is to find a sequence of nodes from $V$, called a burning sequence, to burn the whole graph. This is a discrete-step process, and at each step, an unburned vertex is selected as an…
Querying the shortest path between two vertexes is a fundamental operation in a variety of applications, which has been extensively studied over static road networks. However, in reality, the travel costs of road segments evolve over time,…
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…
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…
We analyze a tree search problem with an underlying Markov decision process, in which the goal is to identify the best action at the root that achieves the highest cumulative reward. We present a new tree policy that optimally allocates a…
Many recent approximation algorithms for different variants of the traveling salesman problem (asymmetric TSP, graph TSP, s-t-path TSP) exploit the well-known fact that a solution of the natural linear programming relaxation can be written…
The emerging edge computing paradigm promises to deliver superior user experience and enable a wide range of Internet of Things (IoT) applications. In this work, we propose a new market-based framework for efficiently allocating resources…
We introduce a novel algorithm for solving network utility maximization (NUM) problems that arise in resource allocation schemes over networks with known safety-critical constraints, where the constraints form an arbitrary convex and…
In the Telephone Broadcasting problem, the goal is to disseminate a message from a given source vertex of an input graph to all other vertices in the minimum number of rounds, where at each round, an informed vertex can send the message to…
In the unsplittable flow problem on a path, we are given a capacitated path $P$ and $n$ tasks, each task having a demand, a profit, and start and end vertices. The goal is to compute a maximum profit set of tasks, such that for each edge…
Moss and Rabani[12] study constrained node-weighted Steiner tree problems with two independent weight values associated with each node, namely, cost and prize (or penalty). They give an O(log n)-approximation algorithm for the…
Tolling, or congestion pricing, has emerged as an effective tool for preventing gridlock in traffic systems. However, tolls are currently mostly designed on route-based traffic assignment models (TAM), which may be unrealistic and…
Identifying shortest paths between nodes in a network is a common graph analysis problem that is important for many applications involving routing of resources. An adversary that can manipulate the graph structure could alter traffic…
We consider a robust version of the revenue maximization problem, where a single seller wishes to sell $n$ items to a single unit-demand buyer. In this robust version, the seller knows the buyer's marginal value distribution for each item…