We introduce two new classes of graphs which we call convex-round, respectively concave-round graphs. Convex-round (concave-round) graphs are those graphs whose vertices can be circularly enumerated so that the (closed) neighborhood of each vertex forms an interval in the enumeration. Hence the two classes transform into each other by taking complements. We show that both classes of graphs have...

The on-line shortest path problem is considered under various models of partial monitoring. Given a weighted directed acyclic graph whose edge weights can change in an arbitrary (adversarial) way, a decision maker has to choose in each round of a game a path between two distinguished vertices such that the loss of the chosen path (defined as the sum of the weights of its composing edges) be as ...

Searching for optimal ways in a network is an important task in multiple application areas such as social networks, co-citation graphs or road networks. In the majority of applications, each edge in a network is associated with a certain cost and an optimal way minimizes the cost while fulfilling a certain property, e.g connecting a start and a destination node. In this paper, we want to extend...

Ginsburg and Sands defined a procedure for completely disconnecting graphs: each round, remove at most one edge from each component and at most w edges total. Define fw(g) to be the minimal number of rounds to reduce G to isolated vertices. Prior work of Ginsburg and Sands has determined fw(Pn) for 2 ≤ w ≤ ∞ and the lead-term asymptotics of f∞(Kn) and f2(Kn)). We show that when T is a tree with...

The graph (non-)planarity game is played on the complete graph Kn between an Enforcer and an Avoider, each of whom take one edge per round. The game ends when the edges chosen by Avoider form a non-planar subgraph. We show that Avoider can play for 3n− 26 turns, improving the previous bound of 3n− 28 √ n.

We tested the adhesive response of polymer surfaces structured with arrays of cylindrical fibrils having diameters of 10-20 µm and aspect ratios 1-2.4. Fibrils had two different tip shapes of end-flaps and round edges. A preload-induced mechanical buckling instability of the fibrils was used to switch between the states of adhesion and non-adhesion. Non-adhesion in fibrils with round edges was ...

We give a simple deterministic constant-round algorithm in the congested clique model for reducing the number of edges in a graph to n1+ε while preserving the minimum spanning forest, where ε > 0 is any constant. This implies that in the congested clique model, it is sufficient to improve MST and other connectivity algorithms on graphs with slightly superlinear number of edges to obtain a gener...

Nanoparticle-cell interactions begin with the cellular uptake of the nanoparticles, a process that eventually determines their cellular fate. In the present work, we show that the morphological features of nanodiamonds (NDs) affect both the anchoring and internalization stages of their endocytosis. While a prickly ND (with sharp edges/corners) has no trouble of anchoring onto the plasma membran...

In this paper, we investigate offline and online algorithms for Round-UFPP, the problem of minimizing the number of rounds required to schedule a set of unsplittable flows of non-uniform sizes on a given path with non-uniform edge capacities. Round-UFPP is NP-hard and constant-factor approximation algorithms are known under the no bottleneck assumption (NBA), which stipulates that maximum size ...

We present improved deterministic distributed algorithms for a number of well-studied matching problems, which are simpler, faster, more accurate, and/or more general than their known counterparts. The common denominator of these results is a deterministic distributed rounding method for certain linear programs, which is the first such rounding method, to our knowledge. A sampling of our end re...