Published in Proceedings of 49th International Workshop on Graph-Theoretic Concepts in Computer Science (to appear), 2023
We show the problem in NP-hard even when restricted to the class of apex-graphs and show PTAS for minor-free graphs.
Published in Proceedings of 22nd International Conference on Autonomous Agents and Multiagent Systems (to appear), 2023
We studied variants of the problem with some additional restrictions on solutions, that place limits on the efficacy of possible gerrymandering strategies.
Published in Computational Geometry: Theory and Applications (to appear), 2023
We present two principal results, both involving local-search PTASs for geometric covering problems. The first is an approximation to the minimum-sized dominating set for a set of convex homothets, and the second is an approximation to the minimum-sized set cover, where the sets are based on convex pseudodisks.
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Published in Random Structures and Algorithms, 2022
We obtain sufficient conditions for the emergence of spanning and almost-spanning bounded-degree rainbow trees in various host graphs, having their edges colored independently and uniformly at random, using a predetermined palette.
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Published in Proceedings of 38th International Symposium on Computational Geometry, SoCG, 2022
We show that proper minor-closed classes have bounded comparable box dimensions and explore further properties of this notion.
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Published in Proceedings of 36th AAAI Conference on Artificial Intelligence, AAAI, 2022
We show that shortest path reconfiguration problem is intractable, even for relaxed variants. We present efficient algorithms for a few restricted variants. We also generalize the problem to when at most k (for a fixed integer k greater than 2) contiguous vertices on a shortest path can be changed at a time.
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Published in Proceedings of 5th Symposium on Simplicity in Algorithms, SOSA, 2022
We show that the number of distinct discrete derivatives, as opposed to the input size, is a better input parameter to express the complexity of convexity testing. We present a nonadaptive convexity tester with query complexity O(log s/epsilon) and complement it with a nearly matching lower bound.
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Published in Proceedings of 29th Annual European Symposium on Algorithms, ESA, 2021
We give polynomial-time approximation schemes for monotone maximization problems expressible in terms of distances.
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Published in Proceedings of European Conference on Combinatorics, Graph Theory and Applications, EuroComb, 2021
We study this chromatic number for the family of sparse graphs, partial 2-trees, graphs with bounded maximum degree and degeneracy.
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Published in Discrete Applied Mathematics, 2021
We show an 8/5 algorithm for the maximum edge 2-colouring problem when the underlying graph is triangle-free and has a perfect matching. We also show that this algorithm cannot achieve an approximation ratio better than 58/37 on a triangle-free graph that has a perfect matching.
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Published in Discrete Applied Mathematics, 2020
We show a bunch of problems are APX-hard on L-EPG graphs.
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Published in Discrete Mathematics & Theoretical Computer Science, 2017
We show the circular separation dimension of 2-outerplanar graphs and series-parallel graphs is 2.
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Published in Discrete Applied Mathematics, 2016
We prove that if G is a Halin graph then VPG bend-number is 1 and EPG bend-number is 2 and the bound is tight.
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Published in Proceedings of International Conference on Combinatorial Optimization and Applications, 2015
We present two approximation algorithms for the maximum independent set problem over the class of B1-VPG graphs. We also showed NP-completeness of the decision version restricted to unit length equilateral B1-VPG graphs.
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