19 research outputs found

    Graph Connectivity with Noisy Queries

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    Graph connectivity is a fundamental combinatorial optimization problem that arises in many practical applications, where usually a spanning subgraph of a network is used for its operation. However, in the real world, links may fail unexpectedly deeming the networks non-operational, while checking whether a link is damaged is costly and possibly erroneous. After an event that has damaged an arbitrary subset of the edges, the network operator must find a spanning tree of the network using non-damaged edges by making as few checks as possible. Motivated by such questions, we study the problem of finding a spanning tree in a network, when we only have access to noisy queries of the form "Does edge e exist?". We design efficient algorithms, even when edges fail adversarially, for all possible error regimes; 2-sided error (where any answer might be erroneous), false positives (where "no" answers are always correct) and false negatives (where "yes" answers are always correct). In the first two regimes we provide efficient algorithms and give matching lower bounds for general graphs. In the False Negative case we design efficient algorithms for large interesting families of graphs (e.g. bounded treewidth, sparse). Using the previous results, we provide tight algorithms for the practically useful family of planar graphs in all error regimes

    LIPIcs, Volume 274, ESA 2023, Complete Volume

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    LIPIcs, Volume 274, ESA 2023, Complete Volum

    LIPIcs, Volume 258, SoCG 2023, Complete Volume

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    LIPIcs, Volume 258, SoCG 2023, Complete Volum

    Stabilizing Column Generation via Dual Optimal Inequalities with Applications in Logistics and Robotics

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    This work addresses the challenge of stabilizing column generation (CG) via dual optimal inequalities (DOI). We present two novel classes of DOI for the general context of set cover problems. We refer to these as Smooth DOI (S-DOI) and Flexible DOI (F-DOI). S-DOI can be interpreted as allowing for the undercovering of items at the cost of overcovering others and incurring an objective penalty. SDOI leverage the fact that dual values associated with items should change smoothly over space. F-DOI can be interpreted as offering primal objective rewards for the overcovering of items. We combine these DOI to produce a joint class of DOI called Smooth-Flexible DOI (SF-DOI). We apply these DOI to three classical problems in logistics and operations research: the Single Source Capacitated Facility Location Problem, the Capacitated p-Median Problem, and the Capacitated Vehicle Routing Problem. We prove that these DOI are valid and are guaranteed to not alter the optimal solution of CG. We also present techniques for their use in the case of solvingCG with relaxed column restrictions. This work also introduces a CG approach to Multi-Robot Routing (MRR). MRR considers the problem of routing a fleet of robots in a warehouse to collectively complete a set of tasks while prohibiting collisions. We present two distinct formulations that tackle unique problem variants. The first we model as a set packing problem, while the second we model as a set cover problem. We show that the pricing problem for both approaches amounts to an elementary resource constrained shortest path problem (ERCSPP); an NP-hard problem commonly studied in other CG problem contexts. We present an efficient implementation of our CG approach that radically reduces the state size of the ERCSPP. Finally, we present a novel heuristic algorithm for solving the ERCSPP and offer probabilistic guarantees forits likelihood to deliver the optimal solution

    27th Annual European Symposium on Algorithms: ESA 2019, September 9-11, 2019, Munich/Garching, Germany

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    29th International Symposium on Algorithms and Computation: ISAAC 2018, December 16-19, 2018, Jiaoxi, Yilan, Taiwan

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    Non-acyclicity of coset lattices and generation of finite groups

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