Related papers: Dynamic Necklace Splitting
Fair graph clustering is crucial for ensuring equitable representation and treatment of diverse communities in network analysis. Traditional methods often ignore disparities among social, economic, and demographic groups, perpetuating…
We revisit the classic problem of dynamically maintaining shortest paths between all pairs of nodes of a directed weighted graph. The allowed updates are insertions and deletions of nodes and their incident edges. We give worst-case…
We study the computational complexity of fair division of indivisible items in an enriched model: there is an underlying graph on the set of items. And we have to allocate the items (i.e., the vertices of the graph) to a set of agents in…
Fair division is the problem of dividing one or several goods amongst two or more agents in a way that satisfies a suitable fairness criterion. These Notes provide a succinct introduction to the field. We cover three main topics. First, we…
The classic cake-cutting problem provides a model for addressing fair and efficient allocation of a divisible, heterogeneous resource (metaphorically, the cake) among agents with distinct preferences. Focusing on a standard formulation of…
In this paper, we focus on how to dynamically allocate a divisible resource fairly among n players who arrive and depart over time. The players may have general heterogeneous valuations over the resource. It is known that the exact…
Decision making problems are typically concerned with maximizing efficiency. In contrast, we address problems where there are multiple stakeholders and a centralized decision maker who is obliged to decide in a fair manner. Different…
In this paper, we propose a distributed algorithm for the minimum dominating set problem. For some especial networks, we prove theoretically that the achieved answer by our proposed algorithm is a constant approximation factor of the exact…
Recent advances in dynamic graph processing have enabled the analysis of highly dynamic graphs with change at rates as high as millions of edge changes per second. Solutions in this domain, however, have been demonstrated only for…
We present the Douglas-Rachford algorithm as a successful heuristic for solving graph coloring problems. Given a set of colors, these type of problems consist in assigning a color to each node of a graph, in such a way that every pair of…
We present dynamic algorithms with polylogarithmic update time for estimating the size of the maximum matching of a graph undergoing edge insertions and deletions with approximation ratio strictly better than $2$. Specifically, we obtain a…
The field of dynamic graph algorithms aims at achieving a thorough understanding of real-world networks whose topology evolves with time. Traditionally, the focus has been on the classic sequential, centralized setting where the main…
The classical house allocation problem involves assigning $n$ houses (or items) to $n$ agents according to their preferences. A key criterion in such problems is satisfying some fairness constraints such as envy-freeness. We consider a…
We study an online version of the max-min fair allocation problem for indivisible items. In this problem, items arrive one by one, and each item must be allocated irrevocably on arrival to one of $n$ agents, who have additive valuations for…
We present a new approach to randomized distributed graph coloring that is simpler and more efficient than previous ones. In particular, it allows us to tackle the $(\operatorname{deg}+1)$-list-coloring (D1LC) problem, where each node $v$…
This paper introduces a natural generalization of the classical edge coloring problem in graphs that provides a useful abstraction for two well-known problems in multicast switching. We show that the problem is NP-hard and evaluate the…
Blockchain uses the idea of storing transaction data in the form of a distributed ledger wherein each node in the network stores a current copy of the sequence of transactions in the form of a hash chain. This requirement of storing the…
The stable marriage and stable roommates problems have been extensively studied due to their high applicability in various real-world scenarios. However, it might happen that no stable solution exists, or stable solutions do not meet…
Current algorithms for large-scale industrial optimization problems typically face a trade-off: they either require exponential time to reach optimal solutions, or employ problem-specific heuristics. To overcome these limitations, we…
This paper provides an algorithmic framework for obtaining fast distributed algorithms for a highly-dynamic setting, in which *arbitrarily many* edge changes may occur in each round. Our algorithm significantly improves upon prior work in…