Related papers: Low-complexity non-uniform demand multicast networ…
The minimum sum coloring problem with bundles was introduced by Darbouy and Friggstad (SWAT 2024) as a common generalization of the minimum coloring problem and the minimum sum coloring problem. During their presentation, the following open…
In this paper, we study robust transshipment under consistent flow constraints. We consider demand uncertainty represented by a finite set of scenarios and characterize a subset of arcs as so-called fixed arcs. In each scenario, we require…
Problems related to network coding for acyclic, instantaneous networks (where the edges of the acyclic graph representing the network are assumed to have zero-delay) have been extensively dealt with in the recent past. The most prominent of…
One of the main theoretical motivations for the emerging area of network coding is the achievability of the max-flow/min-cut rate for single source multicast. This can exceed the rate achievable with routing alone, and is achievable with…
The robust minimum cost flow problem under consistent flow constraints (RobMCF$\equiv$) is a new extension of the minimum cost flow (MCF) problem. In the RobMCF$\equiv$ problem, we consider demand and supply that are subject to uncertainty.…
Network flow interdiction analysis studies by how much the value of a maximum flow in a network can be diminished by removing components of the network constrained to some budget. Although this problem is strongly NP-complete on general…
In recent years many algorithms have been developed for finding patterns in graphs and networks. A disadvantage of these algorithms is that they use subgraph isomorphism to determine the support of a graph pattern; subgraph isomorphism is a…
Minimal multicast networks are fascinating and efficient combinatorial objects, where the removal of a single link makes it impossible for all receivers to obtain all messages. We study the structure of such networks, and prove some…
We consider single-sink network flow problems. An instance consists of a capacitated graph (directed or undirected), a sink node $t$ and a set of demands that we want to send to the sink. Here demand $i$ is located at a node $s_i$ and…
We consider an undirected multi(commodity)flow demand problem in which a supply graph is planar, each source-sink pair is located on one of three specified faces of the graph, and the capacities and demands are integer-valued and Eulerian.…
We study index-coding problems (one sender broadcasting messages to multiple receivers) where each message is requested by one receiver, and each receiver may know some messages a priori. This type of index-coding problems can be fully…
We give an overview of recent developments in the problem of reconstructing a band-limited signal from non-uniform sampling from a numerical analysis view point. It is shown that the appropriate design of the finite-dimensional model plays…
We resolve the question of optimality for a well-studied packetized implementation of random linear network coding, called PNC. In PNC, in contrast to the classical memoryless setting, nodes store received information in memory to later…
The two-sender unicast index coding problem consists of finding optimal coded transmissions from the two senders which collectively know the messages demanded by all the receivers. Each receiver demands a unique message. One important class…
We present a graph theoretic upper bound on speedup needed to achieve 100% throughput in a multicast switch using network coding. By bounding speedup, we show the equivalence between network coding and speedup in multicast switches - i.e.…
NP-complete problems should be hard on some instances but those may be extremely rare. On generic instances many such problems, especially related to random graphs, have been proven easy. We show the intractability of random instances of a…
The chromatic number of signed graphs is defined recently. The coloring and clique problem of interval graphs has been studied and polynomial time algorithms are established. Here we consider these problems for signed interval graphs and…
In unsplittable network flow problems, certain nodes must satisfy a combinatorial requirement that the incoming arc flows cannot be split or merged when routed through outgoing arcs. This so-called "no-split no-merge" requirement arises in…
Robust optimization is concerned with constructing solutions that remain feasible also when a limited number of resources is removed from the solution. Most studies of robust combinatorial optimization to date made the assumption that every…
In this paper, we consider networks with multiple unicast sessions. Generally, non-linear network coding is needed to achieve the whole rate region of network coding. Yet, there exist networks for which routing is sufficient to achieve the…