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Weighted 2-sections and hypergraph reconstruction
PublikacjaIn the paper we introduce the notion of weighted 2-sections of hypergraphs with integer weights and study the following hypergraph reconstruction problems: (1) Given a weighted graph , is there a hypergraph H such that is its weighted 2-section? (2) Given a weighted 2-section , find a hypergraph H such that is its weighted 2-section. We show that (1) is NP-hard even if G is a complete graph or integer weights w does not exceed...
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Chromatic cost coloring of weighted bipartite graphs
PublikacjaGiven a graph G and a sequence of color costs C, the Cost Coloring optimization problem consists in finding a coloring of G with the smallest total cost with respect to C. We present an analysis of this problem with respect to weighted bipartite graphs. We specify for which finite sequences of color costs the problem is NP-hard and we present an exact polynomial algorithm for the other finite sequences. These results are then extended...
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Distributed graph searching with a sense of direction
PublikacjaIn this work we consider the edge searching problem for vertex-weighted graphs with arbitrarily fast and invisible fugitive. The weight function w provides for each vertex v the minimum number of searchers required to guard v, i.e., the fugitive may not pass through v without being detected only if at least w(v) searchers are present at v. This problem is a generalization of the classical edge searching problem, in which one has...
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Network Approach to Increments of RR-intervals for Visualization of Dynamics of Cardiac Regulation
PublikacjaThe transition network for RR -increments is pre- sented in a directed and weighted graph, with vertices represent- ing RR -increments and edges corresponding to the order in a sequence of increments. The adjacency matrix and the transition matrix of this network provide a graphical tool which could be useful in the assessment of cardiac regulation. As an example, the method is applied in detecting differences between diurnal activity...
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Eventual Convergence of the Reputation-Based Algorithm in IoT Sensor Networks
PublikacjaUncertainty in dense heterogeneous IoT sensor networks can be decreased by applying reputation-inspired algorithms, such as the EWMA (Exponentially Weighted Moving Average) algorithm, which is widely used in social networks. Despite its popularity, the eventual convergence of this algorithm for the purpose of IoT networks has not been widely studied, and results of simulations are often taken in lieu of the more rigorous proof....
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Rendezvous of heterogeneous mobile agents in edge-weighted networks
PublikacjaWe introduce a variant of the deterministic rendezvous problem for a pair of heterogeneous agents operating in an undirected graph, which differ in the time they require to traverse particular edges of the graph. Each agent knows the complete topology of the graph and the initial positions of both agents. The agent also knows its own traversal times for all of the edges of the graph, but is unaware of the corresponding traversal...
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Rendezvous of Heterogeneous Mobile Agents in Edge-Weighted Networks
PublikacjaWe introduce a variant of the deterministic rendezvous problem for a pair of heterogeneous agents operating in an undirected graph, which differ in the time they require to traverse particular edges of the graph. Each agent knows the complete topology of the graph and the initial positions of both agents. The agent also knows its own traversal times for all of the edges of the graph, but is unaware of the corresponding traversal...
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Total Completion Time Minimization for Scheduling with Incompatibility Cliques
PublikacjaThis paper considers parallel machine scheduling with incompatibilities between jobs. The jobs form a graph equivalent to a collection of disjoint cliques. No two jobs in a clique are allowed to be assigned to the same machine. Scheduling with incompatibilities between jobs represents a well-established line of research in scheduling theory and the case of disjoint cliques has received increasing attention in recent...
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A Framework for Searching in Graphs in the Presence of Errors
PublikacjaWe consider a problem of searching for an unknown target vertex t in a (possibly edge-weighted) graph. Each vertex-query points to a vertex v and the response either admits that v is the target or provides any neighbor s of v that lies on a shortest path from v to t. This model has been introduced for trees by Onak and Parys [FOCS 2006] and for general graphs by Emamjomeh-Zadeh et al. [STOC 2016]. In the latter, the authors provide...
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Brief Announcement: Energy Constrained Depth First Search
PublikacjaDepth first search is a natural algorithmic technique for constructing a closed route that visits all vertices of a graph. The length of such route equals, in an edge-weighted tree, twice the total weight of all edges of the tree and this is asymptotically optimal over all exploration strategies. This paper considers a variant of such search strategies where the length of each route is bounded by a positive integer B (e.g. due...
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Scheduling of compatible jobs on parallel machines
PublikacjaThe dissertation discusses the problems of scheduling compatible jobs on parallel machines. Some jobs are incompatible, which is modeled as a binary relation on the set of jobs; the relation is often modeled by an incompatibility graph. We consider two models of machines. The first model, more emphasized in the thesis, is a classical model of scheduling, where each machine does one job at time. The second one is a model of p-batching...
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A space-efficient algorithm for computing the minimum cycle mean in a directed graph
PublikacjaAn algorithm is introduced for computing the minimum cycle mean in a strongly connected directed graph with n vertices and m arcs that requires O(n) working space. This is a considerable improvement for sparse graphs in comparison to the classical algorithms that require O(n^2) working space. The time complexity of the algorithm is still O(nm). An implementation in C++ is made publicly available at http://www.pawelpilarczyk.com/cymealg/.