Online graph coloring against a randomized adversary

Electronic version of an article published as Online graph coloring against a randomized adversary. "International journal of foundations of computer science", 1 Juny 2018, vol. 29, núm. 4, p. 551-569. DOI:10.1142/S0129054118410058 © 2018 copyright World Scientific Publishing Company. https://www.worldscientific.com/doi/abs/10.1142/S0129054118410058We consider an online model where an adversary constructs a set of 2s instances S instead of one single instance. The algorithm knows S and the adversary will choose one instance from S at random to present to the algorithm. We further focus on adversaries that construct sets of k-chromatic instances. In this setting, we provide upper and lower bounds on the competitive ratio for the online graph coloring problem as a function of the parameters in this model. Both bounds are linear in s and matching upper and lower bound are given for a specific set of algorithms that we call “minimalistic online algorithms”.Peer ReviewedPostprint (author's final draft

Exact algorithms for maximum transitive subgraph problem

We study the problem of computing a Maximum Transitive Subgraph (MTS) of a given directed graph. This problem is known to be NP-hard. We give an algorithm that runs in time O(4k2n2) to output an MTS for a graph with treewidth k

How Fast Can We Play Tetris Greedily With Rectangular Pieces?

Consider a variant of Tetris played on a board of width $w$ and infinite height, where the pieces are axis-aligned rectangles of arbitrary integer dimensions, the pieces can only be moved before letting them drop, and a row does not disappear once it is full. Suppose we want to follow a greedy strategy: let each rectangle fall where it will end up the lowest given the current state of the board. To do so, we want a data structure which can always suggest a greedy move. In other words, we want a data structure which maintains a set of $O(n)$ rectangles, supports queries which return where to drop the rectangle, and updates which insert a rectangle dropped at a certain position and return the height of the highest point in the updated set of rectangles. We show via a reduction to the Multiphase problem [P\u{a}tra\c{s}cu, 2010] that on a board of width $w=\Theta(n)$, if the OMv conjecture [Henzinger et al., 2015] is true, then both operations cannot be supported in time $O(n^{1/2-\epsilon})$ simultaneously. The reduction also implies polynomial bounds from the 3-SUM conjecture and the APSP conjecture. On the other hand, we show that there is a data structure supporting both operations in $O(n^{1/2}\log^{3/2}n)$ time on boards of width $n^{O(1)}$, matching the lower bound up to a $n^{o(1)}$ factor.Comment: Correction of typos and other minor correction

Recent Advances in Fully Dynamic Graph Algorithms

In recent years, significant advances have been made in the design and analysis of fully dynamic algorithms. However, these theoretical results have received very little attention from the practical perspective. Few of the algorithms are implemented and tested on real datasets, and their practical potential is far from understood. Here, we present a quick reference guide to recent engineering and theory results in the area of fully dynamic graph algorithms

Monotone Drawings of kk-Inner Planar Graphs

A $k$-inner planar graph is a planar graph that has a plane drawing with at most $k$ {internal vertices}, i.e., vertices that do not lie on the boundary of the outer face of its drawing. An outerplanar graph is a $0$-inner planar graph. In this paper, we show how to construct a monotone drawing of a $k$-inner planar graph on a $2(k+1)n \times 2(k+1)n$ grid. In the special case of an outerplanar graph, we can produce a planar monotone drawing on a $n \times n$ grid, improving previously known results.Comment: Appears in the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018). Revised introductio

Dynamic tree shortcut with constant degree

LNCS v.9188 entitled: Computing and Combinatorics: 21st International Conference, COCOON 2015, Beijing, China, August 4-6, 2015, ProceedingsGiven a rooted tree with n nodes, the tree shortcut problem is to add a set of shortcut edges to the tree such that the shortest path from each node to any of its ancestors is of length O(log n) and the degree increment of each node is constant. We consider in this paper the dynamic version of the problem, which supports node insertion and deletion. For insertion, a node can be inserted as a leaf node or an internal node by sub-dividing an existing edge. For deletion, a leaf node can be deleted, or an internal node can be merged with its single child. We propose an algorithm that maintains a set of shortcut edges in O(log n) time for an insertion or deletion.postprin

Computer Science 2019 APR Self-Study & Documents

UNM Computer Science APR self-study report and review team report for Spring 2019, fulfilling requirements of the Higher Learning Commission

Enhancing Privacy Protection:Set Membership, Range Proofs, and the Extended Access Control

Privacy has recently gained an importance beyond the field of cryptography. In that regard, the main goal behind this thesis is to enhance privacy protection. All of the necessary mathematical and cryptographic preliminaries are introduced at the start of this thesis. We then show in Part I how to improve set membership and range proofs, which are cryptographic primitives enabling better privacy protection. Part II shows how to improve the standards for Machine Readable Travel Documents (MRTDs), such as biometric passports. Regarding set membership proofs, we provide an efficient protocol based on the Boneh-Boyen signature scheme. We show that alternative signature schemes can be used and we provide a general protocol description that can be applied for any secure signature scheme. We also show that signature schemes in our design can be replaced by cryptographic accumulators. For range proofs, we provide interactive solutions where the range is divided in a base u and the u-ary digits are handled by one of our set membership proofs. A general construction is also provided for any set membership proof. We additionally explain how to handle arbitrary ranges with either two range proofs or with an improved solution based on sumset representation. These efficient solutions achieve, to date, the lowest asymptotical communication load. Furthermore, this thesis shows that the first efficient non-interactive range proof is insecure. This thesis thus provides the first efficient and secure non-interactive range proof. In the case of MRTDs, two standards exist: one produced by the International Civil Aviation Organization (ICAO) and the other by the European Union, which is called the Extended Access Control (EAC). Although this thesis focuses on the EAC, which is supposed to solve all privacy concerns, it shows that both standards fail to provide complete privacy protection. Lastly, we provide several solutions to improve them

KINE[SIS]TEM'17 From Nature to Architectural Matter

Kine[SiS]tem – From Kinesis + System. Kinesis is a non-linear movement or activity of an organism in response to a stimulus. A system is a set of interacting and interdependent agents forming a complex whole, delineated by its spatial and temporal boundaries, influenced by its environment. How can architectural systems moderate the external environment to enhance comfort conditions in a simple, sustainable and smart way? This is the starting question for the Kine[SiS]tem’17 – From Nature to Architectural Matter International Conference. For decades, architectural design was developed despite (and not with) the climate, based on mechanical heating and cooling. Today, the argument for net zero energy buildings needs very effective strategies to reduce energy requirements. The challenge ahead requires design processes that are built upon consolidated knowledge, make use of advanced technologies and are inspired by nature. These design processes should lead to responsive smart systems that deliver the best performance in each specific design scenario. To control solar radiation is one key factor in low-energy thermal comfort. Computational-controlled sensor-based kinetic surfaces are one of the possible answers to control solar energy in an effective way, within the scope of contradictory objectives throughout the year.FC