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 Computational Geometry: Theory and Applications, 2022
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 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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