On the Power of Advice and Randomization for Online Bipartite Matching

While randomized online algorithms have access to a sequence of uniform random bits, deterministic online algorithms with advice have access to a sequence of advice bits, i.e., bits that are set by an all powerful oracle prior to the processing of the request sequence. Advice bits are at least as helpful as random bits, but how helpful are they? In this work, we investigate the power of advice bits and random bits for online maximum bipartite matching (MBM). The well-known Karp-Vazirani-Vazirani algorithm is an optimal randomized $(1-\frac{1}{e})$-competitive algorithm for \textsc{MBM} that requires access to $\Theta(n \log n)$ uniform random bits. We show that $\Omega(\log(\frac{1}{\epsilon}) n)$ advice bits are necessary and $O(\frac{1}{\epsilon^5} n)$ sufficient in order to obtain a $(1-\epsilon)$-competitive deterministic advice algorithm. Furthermore, for a large natural class of deterministic advice algorithms, we prove that $\Omega(\log \log \log n)$ advice bits are required in order to improve on the $\frac{1}{2}$-competitiveness of the best deterministic online algorithm, while it is known that $O(\log n)$ bits are sufficient. Last, we give a randomized online algorithm that uses $c n$ random bits, for integers $c \ge 1$, and a competitive ratio that approaches $1-\frac{1}{e}$ very quickly as $c$ is increasing. For example if $c = 10$, then the difference between $1-\frac{1}{e}$ and the achieved competitive ratio is less than $0.0002$

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

Klimatski skokovi i više-dekadna promjenjivost pelagičkog ekosustava Jadrana

In recent highly variable climate, a combined effect of a large-scale northern hemisphere climate and regional-scale Adriatic hydroclimate changes significantly reflected in the Adriatic Sea ecosystem. To clarify this statement we set up in connection two inter-annual systems: the air-sea interconnected system and pelagic ecosystems for the period 1961 to 2010. Within this period, significant changes occurred through 1987-1998 period, characterized by a drop of temperature, salinity and oxygen concentration in the middle Adriatic intermediate layer as consequence of a weaker ventilation of the Adriatic Sea. The pelagic ecosystem reacted to these changes. Large fluctuations in marine biota (from plankton to pelagic fish) revealed significantly different regimes before and after the late eighties. Different patterns observed through analyzed biotic parameters seem linked to modification in thermohaline circulation related to the Eastern Mediterranean Transient (EMT), whose effects prevented warmer and saltier water mass intrusions into the Adriatic Sea. These results provide evidence on connections between the shifts in the middle Adriatic pelagic ecosystem and the northern hemisphere climate via changes in regional atmospheric conditions, and highlight the importance of northern hemisphere climate changes for physical and biological regimes of the Adriatic SeaU vrijeme sve izrazitije promjene klime ekosustav Jadranskog mora pod značajnim je utjecajem atmosferskih promjena koje se događaju na sjevernoj hemisferi te na regionalnoj skali Jadrana. U svrhu objašnjenja međuovisnosti ekosustava Jadrana i atmosferskih procesa na različitim prostornim skalama (od hemisferske do regionalne) analizirana je višegodišnja (1961.-2010.) promjen- jivost sustava atmosfera-more i pelagičkog ekosustava. Unutar promatranog vremenskog razdoblja najznačajnija promjena dogodila se između 1987. i 1998. u intermedijalnom sloju srednjeg Jadrana i bila je obilježena padom temperature mora i saliniteta te kisika kao posljedica slabijeg ventiliranja Jadrana. Istovremeno su u ekosustavu pelagijala Jadranskog mora primijećene velike fluktuacije u biomasi morskih organizama (od fitoplanktona do plave ribe). Izdvojena su signifikantno različita stanja ekosustava Jadrana prije i poslije kasnih osamdesetih godina prošlog stoljeća. Uzrok ovim različitim stanjima ekosustava dijelom se može povezati sa modificiranom termohalinom cirkulacijom Jadrana koja je pod utjecajem EMT (Eastern Mediterranean Transient) sprječavala ulazak toplije i slanije vode u Jadransko more, uzrokujući na taj način uočene promjene u ekosustavu. Ovi rezultati dokazuju povezanost između skokova u pelagičkom ekosustavu na području srednjeg Jadrana i klime na sjevernoj hemisferi putem promjena u regionalnim vremenskim uvjetima te ističu važnost utjecaja klimatskih promjena i skokova na fizikalna i biološka stanja Jadranskog mora

Data Dissemination in Unified Dynamic Wireless Networks

We give efficient algorithms for the fundamental problems of Broadcast and Local Broadcast in dynamic wireless networks. We propose a general model of communication which captures and includes both fading models (like SINR) and graph-based models (such as quasi unit disc graphs, bounded-independence graphs, and protocol model). The only requirement is that the nodes can be embedded in a bounded growth quasi-metric, which is the weakest condition known to ensure distributed operability. Both the nodes and the links of the network are dynamic: nodes can come and go, while the signal strength on links can go up or down. The results improve some of the known bounds even in the static setting, including an optimal algorithm for local broadcasting in the SINR model, which is additionally uniform (independent of network size). An essential component is a procedure for balancing contention, which has potentially wide applicability. The results illustrate the importance of carrier sensing, a stock feature of wireless nodes today, which we encapsulate in primitives to better explore its uses and usefulness.Comment: 28 pages, 2 figure

The Complexity of Graph Exploration Games

The graph exploration problem asks a searcher to explore an unknown graph. This problem can be interpreted as the online version of the Traveling Salesman Problem. The treasure hunt problem is the corresponding online version of the shortest s-t-path problem. It asks the searcher to find a specific vertex in an unknown graph at which a treasure is hidden. Recently, the analysis of the impact of a priori knowledge is of interest. In graph problems, one form of a priori knowledge is a map of the graph. We survey the graph exploration and treasure hunt problem with an unlabeled map, which is an isomorphic copy of the graph, that is provided to the searcher. We formulate decision variants of both problems by interpreting the online problems as a game between the online algorithm (the searcher) and the adversary. The map, however, is not controllable by the adversary. The question is, whether the searcher is able to explore the graph fully or find the treasure for all possible decisions of the adversary. We prove the PSPACE-completeness of these games, whereby we analyze the variations which ask for the mere existence of a tour through the graph or path to the treasure and the variations that include costs. Additionally, we analyze the complexity of related problems that ask for a tour in the graph or a s-t path