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Financial networks raise a significant computational challenge in identifying insolvent firms and evaluating their exposure to systemic risk. This task, known as the clearing problem, is computationally tractable when dealing with simple…
This paper introduces a variant of the classical edge coloring problem in graphs that can be applied to an offline scheduling problem for crossbar switches. We show that the problem is NP-complete, develop three lower bounds bounds on the…
Given a weighted graph $G$ with $n$ vertices and $m$ edges, and a positive integer $p$, the Hamiltonian $p$-median problem consists in finding $p$ cycles of minimum total weight such that each vertex of $G$ is in exactly one cycle. We…
Two kinds of approximation algorithms exist for the k-BALANCED PARTITIONING problem: those that are fast but compute unsatisfying approximation ratios, and those that guarantee high quality ratios but are slow. In this paper we prove that…
The concept of clearing or netting, as defined in the glossaries of European Central Bank, has a great impact on the economy of a country influencing the exchanges and the interactions between companies. On short, netting refers to an…
One way to define the Matching Cut problem is: Given a graph $G$, is there an edge-cut $M$ of $G$ such that $M$ is an independent set in the line graph of $G$? We propose the more general Conflict-Free Cut problem: Together with the graph…
We study a large family of graph covering problems, whose definitions rely on distances, for graphs of bounded cyclomatic number (that is, the minimum number of edges that need to be removed from the graph to destroy all cycles). These…
We study the problem of augmenting a weighted graph by inserting edges of bounded total cost while minimizing the diameter of the augmented graph. Our main result is an FPT 4-approximation algorithm for the problem.
Proximity graphs have been studied for several decades, motivated by applications in computational geometry, geography, data mining, and many other fields. However, the computational complexity of classic graph problems on proximity graphs…
In this paper, we study the parameterized complexity and inapproximability of the {\sc Induced Matching} problem in hamiltonian bipartite graphs. We show that, given a hamiltonian cycle in a hamiltonian bipartite graph, the problem is…
We study the Second Price Matching problem, introduced by Azar, Birnbaum, Karlin, and Nguyen in 2009. In this problem, a bipartite graph (bidders and goods) is given, and the profit of a matching is the number of matches containing a second…
The length-constrained cycle partition problem (LCCP) is a graph optimization problem in which a set of nodes must be partitioned into a minimum number of cycles. Every node is associated with a critical time and the length of every cycle…
We study a natural generalization of the maximum weight many-to-one matching problem. We are given an undirected bipartite graph $G= (A \cup P, E)$ with weights on the edges in $E$, and with lower and upper quotas on the vertices in $P$. We…
In the Strip Packing problem, we are given a vertical strip of fixed width and unbounded height, along with a set of axis-parallel rectangles. The task is to place all rectangles within the strip, without overlaps, while minimizing the…
In this paper, we consider the maximum $k$-edge-colorable subgraph problem. In this problem we are given a graph $G$ and a positive integer $k$, the goal is to take $k$ matchings of $G$ such that their union contains maximum number of…
A large number of applications such as querying sensor networks, and analyzing protein-protein interaction (PPI) networks, rely on mining uncertain graph and hypergraph databases. In this work we study the following problem: given an…
Given a linear ordering of the vertices of a graph, the cutwidth of a vertex $v$ with respect to this ordering is the number of edges from any vertex before $v$ (including $v$) to any vertex after $v$ in this ordering. The cutwidth of an…
We introduce a `concrete complexity' model for studying algorithms for matching in bipartite graphs. The model is based on the "demand query" model used for combinatorial auctions. Most (but not all) known algorithms for bipartite matching…
Motivated by the analogous questions in graphs, we study the complexity of coloring and stable set problems in hypergraphs with forbidden substructures and bounded edge size. Letting $\nu(G)$ denote the maximum size of a matching in $H$, we…
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…